# Study Guide Algebra. Line, numb, fit, model, time.

Consider the equation 3p – 7 + p = 13. What is the resulting equation after the first step in the solution?
4p – 7 = 13
Fiona solved the equation shown. What is the missing step of her solution?
Simplify by combining like terms
Which input value produces the same output value for the two functions on the graph? G1
Check Graph #1 in notebook
x=1
Consider the functions shown on the graph. What is the input value for which the statement f(x) = g(x) is true? G2
Check graph #2
1.5
Solve the equation.
−10x + 1 + 7x = 37
x = −12
Rahul solved the equation 2(x – ) – x = . In which step did he use the addition property of equality?
Step 3
The Apache Taxi Company charges \$2.50 to pick up a passenger and then adds \$1.95 per mile. Isaac was charged \$27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?
1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.
Which input value produces the same output value for the two functions on the graph? GRAPH3
x-2 G3
What is the solution to the linear equation?
2/5 + p = 4/5 + 3/5p
P=1

Solve the equation.

-3x + 1 + 10x = x + 4

X=1/2
The International Business Club starts the school year with \$250.50 in their account. They spend \$35 each month on activities. The Future Agricultural Leaders Club starts with \$300 and spends \$45.25 each month.Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?
250.5 – 35m = 300 – 45.25m

What is the solution to the linear equation?

6k + 10.5 = 3k + 12

k=0.5

What is the solution to the linear equation?

d – 10 – 2d + 7 = 8 + d – 10 – 3d

d=1
Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
-3/4m-1/2=2+1/4m
4

What is the solution to the linear equation?

2.8y + 6 + 0.2y = 5y – 14

y=10
How many solutions exist for the given equation? 3(x – 2) = 22 – x
One
Which equation can be used to represent “three minus the difference of a number and one equals one-half of the difference of three times the same number and four”?
3 – (n – 1) = 1/2(3n – 4)
Which equation has no solution?
5 + 2(3 + 2x) = x + 3(x + 1)

How many solutions exist for the given equation?

1/2(x + 12) = 4x – 1

One
What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?
4

How many solutions exist for the given equation?

12x + 1 = 3(4x + 1) – 2

infinitely many

Solve for n.

n + 1 = 4(n – 8)

n=11
Karissa begins to solve the equation 1/2(x – 14) + 11 = 1/2x – (x – 4). Her work is correct and is shown below. When she subtracts 4 from both sides, x = -x results. What is the value of ?
How many solutions exist for the given equation?
one
Which equation can be used to represent “three minus the difference of a number and one equals one-half of the difference of three times the same number and four”?
3 – (n – 1) =1/2 (3n – 4)

How many solutions exist for the given equation?

1/2(x + 12) = 4x – 1

one
What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?
4

How many solutions exist for the given equation?

12x + 1 = 3(4x + 1) – 2

infinitely many

Solve for n.

n + 1 = 4(n – 8)

n=11
Karissa begins to solve the equation 1/2(x – 14) + 11 = 1/2x – (x – 4). Her work is correct and is shown below.
Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?
60t + 55t = 150
Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?
18 minutes
Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?
Check notebook. RUN/BIKE graph
It takes 5 minutes to fill the sink using only the cold water. If both the hot water and the cold water are turned on, it takes 2 minutes to fill the sink. Which is the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water?
Check notebook. HOT/COLD graph.
If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours.
1/3
Lea and Marie are washing all the windows in their house. It would take Lea 80 minutes to wash the windows by herself, and it would take Marie 60 minutes to wash them by herself. Lea creates a table so she can find out how long it will take to wash the windows if they work together. What is the missing value in the table that represents the rate for Marie?
1/60
Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone. What is the value of r, the part of the job that Marina can complete in 1 hour?
0.4
It would take Marco 6 hours to paint a fence by himself. It would take Jaylyn 5 hours to paint the same fence by herself. Marco is creating this table to help him determine how long it would take them to paint the fence together. Which heading should be written above the first column of numbers?
Rate (part/hour)
The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis. Which is an equivalent equation solved for the slope, m?
m=y-b/x
The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved for r is r = .
r = 8
In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. She writes the equation as F = ma, then realizes that each of her homework problems asks her to solve for acceleration. She rewrites the formula as f/m = a. Using this formula, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms? Express your answer to the nearest tenth.
2.2 m/s^2

Solve for a.

7a – 2b = 5a + b

a=3/2b
Marta is solving the equation S = 2Πrh + 2Πr2 for h. Which should be the result?
S/2(pi)r – r = h
The goals against average (A) for a professional hockey. hich is an equivalent equation solved for g?
At/60=g
The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is
C = K – 273.15

Solve for k.

8k + 2m = 3m + k

k = m/7

Solve the equation for a.

K = 4a + 9ab

a=k/4+9b
Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h?
h = (p/0.7- b)÷ r
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
Notes. Line graph Name3
Step 1: Subtract 3 from both sides of the inequality.
Step 2: __________
Step 3: Divide both sides of the inequality by the coefficient of x.What is the missing step in solving the inequality 5 – 8x < 2x + 3?

Add 8x to both sides of the inequality.
What value of x is in the solution set of 8x – 6 > 12 + 2x?
5
Which is a correct first step in solving the inequality -4(2x – 1) > 5 – 3x?
Distribute -4 to get -8x + 4 > 5 – 3x.
What value of x is in the solution set of 4x – 12 ≤ 16 + 8x?
-7
What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?
-1
Which number line represents the solution set for the inequality -1/2x ≥ 4?
Notes Line graph Name 8
What value of x is in the solution set of 3(x – 4) ≥ 5x + 2?
-10

Solve the inequality.

2(4x – 3) ≥ -3(3x) + 5x?

x ≥ 0.5
The solution is n = -2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification?
-0.8 = -0.8

Solve the equation.

2x − 3 + 4x = 21

x=4
Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?
2v + 4 = 8

How many solutions exist for the given equation?

3(x + 10) + 6 = 3(x + 12)

infinitely many
Which number line represents the solution set for the inequality 3x < -9?
Notes line graph name -3
What interval includes all possible values of x, where -3(6 – 2x) ≥ 4x + 12?
[15, ∞)

Sara wants to find the input value that produces the same output for the functions represented by the tables.

What is the input value that produces the same output value in both charts?

2
What value of x is in the solution set of -2(3x + 2) > -8x + 6?
6

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n – 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = + 2.

Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?

9 sides
Which equation can be used to represent “six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?
6 + 2(x + 4) = 1/2(3 – x)
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Check all that apply.
230p – 1010 = 650p – 400 – p
What is the solution to -4(8 – 3x) ≥ 6x – 8?
x ≥ 4
Nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. In the first part of the race, her average speed was 8.75 kilometers per hour. For the second part of the race, she started to get tired, so her average speed dropped to 6 kilometers per hour. Which expression represents Nikita’s distance for the second part of the race?
6(0.65 – t)
Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x – 4.75) = 629.9. She left out the description for the last step.
Divide both sides of the equation by 10.4.
Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
1/4(x) = (30 + 60)
Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of \$3 tickets purchased?
graph in notes Name \$3 ti ckets
Each day that a library book is kept past its due date, a \$0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?
(8, 2.40)
Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let y represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, t? Is the graph of the equation continuous or discrete?
t=4y+7.75; continuous
The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes.
\$100
What is the lowest value of the range of the function shown on the graph?
See graph 3,-2 in notes
-2

What is the range of the given function?

{(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}

{y | y = -9, -3, 0, 5, 7}
What is the range of the given function?
{y | y = -7, -1, 0, 9}
The table shows ordered pairs of the function y = 8 – 2x. When x = 8, the value of y is
Graph y=8-2x
What is the domain of the function shown in the mapping?
{x | x = -5, -3, 1, 2, 6}
Input output graph -3,4
What is the domain of the function on the graph?
all real numbers greater than or equal to -3
Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. What is the range of the function?
all real numbers greater than or equal to 11
Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?
(1, 3)

The function h(t) = -16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot.

What does h(3.2) represent?

the height of the rock 3.2 seconds after it is propelled

The table represents a function.

Which value is an output of the function?

-2

function table in notes

Which is true regarding the graphed function f(x)?
f(5)=-1
The table represents a function. What is f(5)?
-8

The function f(x) is given by the set of ordered pairs.

{(1,0), (-10,2), (0,6), (3,17), (-2,-1)} Which equation is true?

f(0)=6
The function V(r)=4/3(pi)r^3 can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?
The table represents a function. What is f(-2)?
1
If point (4, 5) is on the graph of a function, which equation must be true?
f(4)=5
Hiroto’s texting plan costs \$20 per month, plus \$0.05 per text message that is sent or received. Emilia’s plan costs \$10 per month and \$0.25 per text. Using the graph below, which statement is true?
Both plans cost the same when 50 texts are sent.
Which statement is true regarding the functions on the graph?
f(-3) = g(-3)
What is f(3)?
9
Which statement is true regarding the graphed functions?
f(2) = 0 and g(-2) = 0
View graph EF in notes
Which represents where f(x) = g(x)?
f(2) = g(2) and f(0) = g(0)
GRAPH EF2
When f(x) = -3, what is x?
-1
Which represents where f(x) = g(x)?
f(-4) = g(-4) and f(0) = g(0)
graph EF3
If f(x) = 6x – 4, what is f(x) when x = 8?
44
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function’s values go to negative infinity.
Which statement is true about the graphed function?
F(x) > 0 over the interval (-∞, -4)
What are the x-intercepts of the graphed function?
(-3, 0) and (1,0)
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function’s values go to positive infinity.
Which is a y-intercept of the graphed function?
(0, -9)
Graph 1 in analyzing graphs
Which interval for the graphed function contains the local maximum?
[0, 2]
Which lists all of the y-intercepts of the graphed function
(0, -3)
Which lists all of the x-intercepts of the graphed function?
(1, 0), (2, 0), and (-3, 0)
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
Which is a valid prediction about the continuous function f(x)?
f(x) ≥ 0 over the interval [5, ∞).
Which is a valid prediction about the continuous function f(x)?
f(x) ≥ 0 over the interval [-1, 1].
Which lists all of the y-intercepts of the continuous function in the table?
(0, 0)
Which is a possible turning point for the continuous function f(x)?
(0, -2)
Which is an x-intercept of the continuous function in the table?
(3, 0)
Based on the table, which best predicts the end behavior of the graph of f(x)?
As x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞.
Which is an x-intercept of the continuous function in the table?
(-1, 0)
What are all of the x-intercepts of the continuous function in the table?
(-4, 0), (4, 0)

Adita has two options for how to invest \$1,000.

Plan A: Put the \$1,000 in an account that pays \$100 per year.
Plan B: Put the \$1,000 in an account that pays 5 percent interest per year.

Which statement is true?

Plan A will be worth more than plan B after two years.
What type of graph is shown, and what is the growth factor?
exponential function; growth factor of 4
Which graph represents an exponential function?
LOOK IN NOTES at linear growth #1
Which table represents a linear function?
linear growth #2
What kind of growth model (pattern) is shown in the table?
exponential 3
What is the missing number in the table?

1,296

#4

Which of the following best describes how the y values are changing over each interval?
They are being multiplied by 2 each time.
Over which interval are the exponential and linear function approximately the same?
from 0.75 to 1.0
The table below represents a function.
Which statement would best describe the graph of the function?
The graph starts flat but curves steeply upward.
Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research. Which insect population is growing at a faster rate?
The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week
Which of the following describes the function shown in the table below?
Comparing notes
1
exponential, there is a constant rate of decay or decrease
Which number is missing in the table of values below?
216
g2
3 4 5 6 8 9 10
Which statement best describes the growth rates of the functions below?
The exponential function grows faster than the quadratic function over two intervals; 2<x<4.
Which rule can be used to describe the growth of the y-values of the function mc018-1.jpg over each interval from mc018-2.jpg to mc018-3.jpg?
multiply by 12
A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval mc016-1.jpg?
The exponential function decays at three-fourths the rate of the quadratic function.
Which of the following describes the growth rate of the exponential function in the graph below?
For each x increase of 1, the y increases by a common factor of 3.
What is f(0)?
unit review 1
-6 only

Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers.

To the nearest tenth of a second, how much time would it take the penny to hit the ground?

0.6 seconds
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

Consider the function represented by the graph.

What is the domain of this function?

{x| x >0}

A ball is thrown straight up into the air. The height, in feet, h(t), of the ball collected over t seconds is shown in the table.

Which statement is true?

The maximum height of the ball was 2.5 seconds after it was thrown.
Which ordered pair could be removed so that the set of ordered pairs is a function?
(4, -2)
According to the table, which ordered pair is a local minimum of the function, f(x)?
(0, 9)

The graph represents a functional relationship.

Which value is an input of the function?

4
The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which statement is true?
Seven erasers cost \$3.50.
Which statement is true regarding the functions on the graph?
f(2) = g(2)
Which could be the entire interval over which the function, f(x), is negative?
(-∞, -6)
Which interval for the graphed function contains the local minimum?
g2
[-3, -1]
Analyze the graph of the function f(x) to complete the statement.
F(x) < 0 over the intervals (-∞, -3) and (-1.1,0.9)
Which ordered pair can be removed so that the resulting graph represents a function?
(1,3)
Which graph represents a function?
g3
The table below shows the amount that must be repaid, y, when x dollars are borrowed.
y=5/4x+10
The table below shows the predicted number of words Janae can type, y, in x minutes. Which describes the pattern in the table?
Janae types 30 words each minute.
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
TAbles graph 1
Which table of values corresponds to the graph below?
graph 2
The table below shows the relationship between the approximate number of hours and the corresponding number of days on Saturn.
658 2/3
Four representations of the same data are shown below. Which two representations are considered to be only partial representations?
the verbal description and the graph
Which table of values corresponds to the graph below?
g3
Some states pay \$0.05 for each can that is recycled. Which graph represents the amount of money earned, y, by recycling x cans in these states?
this is a graph- points are 1,20
2,40, 3,60
1 2 3 4 7 8 10
The graph below represents the number of books Jaleel has read over the past x weeks. Which equation represents the graph?
y = 3x

Anderson is a plumber and is paid a fixed amount just to make a house visit. The remainder of his fee, y, is determined by the number of hours that he works, x, as shown below.

Which equation represents the graph?

y = 10x + 50
Which table represents a linear function?
Introduction g1

The graph shows the amount of money Miguel earns after working x hours.

What is the ratio of the change in y-values to the change in x-values for this function?

13:1

The table shows the number of grapes eaten over several minutes.

What is the rate of change for the function on the table?

15 grapes eaten per minute
Which functions have an additive rate of change of 3? Check all that apply.
4,6 is a point
The table shows the distance traveled over time while traveling at a constant speed. What is the ratio of the change in y-values to the change in x-values?
1,200:1
Which table represents a linear function?
g2
A data set contains an independent and dependent variable. Which must be true of the data set if a linear function can be used to represent the data?
The set must have a constant additive rate of change.

The table shows the profit from a school book fair based on the number of books sold.

What is the rate of change for the function represented in the table?

\$1.50
The table below shows measurements (in inches) from cubes with different side lengths. Which pairs of variables have a linear relationship? Check all that apply.
side length and perimeter of 1 face
perimeter of 1 face and area of 1 face
side length and volume

The graph shows the increase in temperature over time in an oven.

What is the change in the y-values and x-values on the graph?

The change in the y-values is 40 and the change in the x-values is 1.
Which relationship has a zero slope?
g1 slope of a line
At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?
The slope of the line will be zero

The graph of a linear function is shown.

Which word describes the slope of the line?

negative
Which graph has a slope of 4/5?
g2

The graph represents the balance on Harrison’s car loan in the months since purchasing the car.

Which statement describes the slope of the line?

Harrison makes a monthly payment of \$250.
The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height. What is the slope of the line?
2

The graph of a linear function is shown.

Which word describes the slope of the line?

zero
g3

The table represents a linear function.

What is the slope of the function?

-6
Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?
Aaron’s rate for mowing lawns is 0.5 acres per hour.

The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:

\$0.50, \$0.65, \$0.80, \$0.95, \$1.10, …

Which equation represents Marisa’s library fine as a function of a book that is n days overdue?

f(n) = 0.15n + 0.35
What is the constant of variation, k, of the direct variation, y = kx, through (-3, 2)?
k = -2/3

Three points of a function are graphed.

Which statement describes the function through the points?

The function is linear but is not a direct variation function.
A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
y = 7x

The velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table.

The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?

9.8 m/s^2
Which graph represents a function with direct variation?
g4

The table represents a bicycle rental cost in dollars as a function of time in hours.

Which explains whether or not the function represents a direct variation?

This function represents a direct variation because it passes through the origin and has a constant rate of change of \$5 per hour.

A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served.

If the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?

t = 1.8g

The pattern of numbers below is an arithmetic sequence:

14, 24, 34, 44, 54, …

Which statement describes the recursive function used to generate the sequence?

The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.

What is the common difference in the following arithmetic sequence?

7, 3, -1, -5, ….

-4
Which of the following is true about the sequence graphed below?
The sequence is arithmetic because the terms have a common difference.
Ms. Clark earned \$29,600 in her third year as a banker and \$32,600 in her seventh year. How much did she make in her tenth year? Assume that her yearly salaries form an arithmetic sequence.
\$34,850
What is the common difference of the arithmetic sequence graphed below?
2
Which of the following is an arithmetic sequence?
1/2,2,7/2,5,…
Which of the following is true regarding the sequence graphed below?
The sequence is not arithmetic because the terms do not have a common difference.
What is the next term in the sequence 58, 47, 36, 25, …?
14
A karate studio charges \$35 for the first course and \$22.50 for each course after that, even if the student leaves the course early. Cena paid \$170 for her son to take courses. How many courses did he take?
7 courses
What is the explicit rule for the arithmetic sequence shown in the graph?
an-9.5+2(n-1)
What is the common difference in the following arithmetic sequence?
11
Which of the following is an arithmetic sequence?
unit review 1
To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
-2/5

The table below shows the amount of money Sarah spends for a craft demonstration.

Number of People Attending
Cost
5\$15
8\$18
10\$20
15\$25

Sarah spends a total of \$60. Based on the information in the table, how many people attended the craft demonstration

50

The table represents a linear function.

What is the slope of the function?

-4
g2 unit review
The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?
The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.
A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?
y=x/3
Javier and his study group designed a word problem, equation, table, and graph that were all supposed to represent the same information, as shown below.
Which piece of information does not represent the same information as the other three parts?
graph
Based on the information in the graph, if David’s bill came to \$66 after the coupon was applied, how much would his bill have been if he hadn’t used the coupon?
\$68
A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?
The line does not represent a direct variation because it does not go through the origin.
Which table represents a linear function?
g3
What is the constant of variation, k, of the line y = kx through (3,18) and (5,30)?
6

Mrs. Jackson gives the table below to her students.

In order for the function to be linear, what must m be and why?

m = 20 because the rate of change is -3.
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
m = 90 – 6d

The table represents the function f(x).

Which function of t has the same slope and y-intercept as f(x)?

f(t) =2/3 t + 4
What are the slope and y-intercept of the linear function graphed to the left?
slope: -1/2; y-intercept: 1
A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf’s height in feet as a function of time, in seconds, after leaving the branch?
graph with point 8,12

A store offers packing and mailing services to customers. This table is given to customers to help them estimate the cost of shipping a box based on its weight in pounds, and a flat rate of \$5 for packing.

Which equation represents the shipping cost as a function of x, the weight in pounds?

f(x) = 2.25x + 5
What is the slope of the line represented by the equation y = -1/2-x +1/4 ?
-1/2
Which equation represents the graphed function?
y=-1/3x+3
Which equation represents the graphed function?
y=-2x+3
Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3
y – 2 = 1/3(x – 3)
What is the slope of the line?
-1/2
Which equation represents a line that passes through (5, 1) and has a slope of 1/2/?
y-1=1/2(x-5)
Which steps should be used to graph the equation y – 4 = (x + 2)?
1. Plot the point (-2,4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
Which linear function represents the line given by the point-slope equation y + 1 = -3(x – 5)?
f(x) = -3x + 14
Alejandra correctly wrote the equation y – 3 =1/5 (x – 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?
y – 3 = 2(x – 10)
Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4 ?
y-1/3+3/4(x-4)
What is the slope of the line?
5/2
points are 0,-1 and 2,4
Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?
m=90-6d

The table represents the function f(x).

Which function of t has the same slope and y-intercept as f(x)?

f(t) =2/3 t + 4
What are the slope and y-intercept of the linear function graphed to the left?
slope:-1/2 ; y-intercept: 1
Which shows a graph of a linear equation in standard form Ax + By = C, where A = 0, B is positive, and C is negative?
g1
Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?
y – 1 = 3x
The graph of the equation x – 2y = 5 has an x-intercept of 5 and a slope of 1/2 . Which shows the graph of this equation?
:Line passes through longitude of 5 and lat of in between -2 & -3
Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
-9

The table represents a linear equation.

Which equation correctly uses point (-2, -6) to write the equation of this line in point-slope form?

y + 6 =2/5 (x + 2)
A line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation y = (x – 2). Which equations also represent this line? Check all that apply.
y = -5/3x+10/3
3y = -5x + 10
5x + 3y = 10
Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)?
f(x) =1/2 x + 4
Which is true of the standard form of the equation of the line graphed?
The value of A can only be 1, the value of C can only be -3, and the value of B is 0.
How does the slope of g(x) compare to the slope of f(x)?
The slope of g(x) is less than the slope of f(x).
What is the equation of the graphed line written in standard form?
x – 4y = 4
What is the equation of the line that is perpendicular to the line y = 6 and passes through the point (-4, -3)?
x = -4
What is the equation of the line in slope-intercept form that is perpendicular to the line y = 3/4x – 2 and passes through the point (-12, 10)?
y = -4/3x – 6
Which equation represents the graphed function?
y=1/4x-2
Timmy writes the equation f(x) = x – 1. He then doubles both of the terms on the right side to create the equation g(x) = x – 2. How does the graph of g(x) compare to the graph of f(x)?
The line of g(x) is steeper and has a lower y-intercept.

Raphael graphed the functions g(x) = x + 2 and f(x) = x – 1. How many units below the y-intercept of g(x) is the y-intercept of f(x)?

The y-intercept of f(x) is

3
MOST RECENT TEST STARTS ON 245

A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic.

Which graph could represent the area of each rectangle in terms of the change in the length and width?

Points located on
0.40 1,45 2,47 8,25

Daniel is on an airplane flying to a destination 825 miles away. After one hour, the pilot announces that the plane is 495 miles away from its destination airport. In another hour, the pilot announces that the plane will begin its half-hour descent for the final 165 miles.

Which equation represents the remaining distance, in miles, to the destination in terms of t, the time, in hours, since leaving the airport?

d = 825 – 330t

The graph shows the population of a bacteria in an experiment, measured every hour.

Which function represents the population of the bacteria after t hours?

f(t) = 10(1.4)t

Alicia bought a notebook and several erasers at the student store. The graph shows the relationship between the total cost of her items and the number of erasers she purchased.

What is the cost of each eraser?

\$1.50

The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours.

Which function can be used to determine the approximate number of grams of the sample remaining after t hours?

y = 50(0.85)x

Sophia plots points on a graph to represent the shape of a concave lens.

Which type of function should Sophia use to model the shape of the lens?

If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y, the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x?
Ppoints 0,15 1,25

Teddy is preparing to sell some wooden blocks at a garage sale. Before pricing individual bags of blocks, he decides to determine the approximate number of blocks per pound by researching the weights of different sets of blocks. The graph shows his data.

About how many blocks are there per pound? Round to the nearest block.

20 blocks
Amanda is studying relationships between the values and ages of different items. She decides to ask teachers at her school to estimate the values and ages of their cars. She will exclude any antique cars and knows that the value of a car depreciates over time. Which correlation is expected between the age and value of a car?
negative

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute.

According to the line of best fit, about how many minutes will it take for the temperature to reach 100°C, the boiling point of water?

5

Mr. Palmer does an experiment to investigate the effects of distractions on studying and learning. He gives each participant a line with 10 words to memorize in 5 minutes. Some of the participants are interrupted during the 5 minutes with text messages from friends. The graph shows the number of words remembered after 5 minutes and the number of text messages sent to the participants as distractions.

According to the line of best fit, about how many words would a person remember if he or she is distracted by 7 text messages?

5 words

The table shows the ages and weights of babies at a hospital.

What is the correlation between age and weight as shown in the table?

positive

Lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. The table shows her data.

According to the line of best fit, about how many times would the coin land heads up in 100 flips?

53

Latitude and longitude describe locations on the Earth with respect to the equator and prime meridian. The table shows the latitude and daily high temperatures on the first day of spring for different locations with the same longitude.

Which statement describes the slope of the line of best fit for the data?

The temperature decreases by about 1.7° for each 1 degree increase north in latitude.
Which table shows a negative correlation?
graph 1 in most recent
Which is most likely the correlation coefficient for the set of data shown?
0.19
Which r-value represents the strongest negative correlation?
-0.7
Which is most likely the correlation coefficient for the set of data shown?
-0.91
Which r-value represents the weakest correlation?
0.11
Which relationships would most likely be causal? Check all that apply.

a positive correlation between the number of homework assignments completed and the grade on the exam

a positive correlation between the temperature in a canyon in the early spring and the number of snakes seen by hikers

What is the correlation coefficient for the data shown in the table?
R=1
Which r-value represents the most moderate correlation?
0.56
Which relationships would most likely be causal? Check all that apply.
a negative correlation between the temperature and the amount of snow still on the ground
a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

The table shows the time a patient spends at the dentist and the amount of the bill.

What is the correlation coefficient for the data in the table?

0.93

The table shows the relationship between time spent running and distance traveled.

Which type of model best describes the relationship?

linear, because the r value for the linear model is closest to 1

Janna is making a prediction of the frequency of a key that is 12 keys from middle C.

Which best describes her prediction?

extrapolation, because a key that is 12 keys from middle C is outside the data set

Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments.

She calculates two regression models. Which is true?

The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.

The table compares x, the number of minutes of television Sam watched each day, to y, the number of minutes she spent exercising. The function y = -0.78x + 95 models the data in the table.

Which is the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day?

72 minutes

The quadratic regression graphed on the coordinate grid represents the height of a road surface x meters from the center of the road.

What does the graph of the regression model show?

The height of the surface decreases from the center out to the sides of the road.

Marta’s mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online.

6,271

The table shows the wavelength of the sound produced by keys on a piano x keys away from the A above middle C.

Using the exponential regression model, which is the best prediction of the wavelength of the key that is 8 above the A above middle C?

49.44

The table shows the population of a small town over time. The function P = 10,550(1.1)x models the population x years after the year 2000.

For which year would this model most likely be sufficient to make a prediction of the population?

2005

The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground.

A line of best fit for the data is represented by h = -21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?

According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants.

According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for \$5?

13

The table shows the height of a candle as it is continuously burned.

Which statement describes the candle?

The candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour.
Which is most likely the correlation coefficient for the set of data shown?
-0.21

A line of best fit is drawn for the set of points shown on the graph.

Which point is an approximate extrapolation for x = 30 from the line of best fit?

(30, 38)

The table shows the value of a savings bond that doubles in value after 5 years.

Which statement describes the bond?

The bond had an original value of \$50 and grows at a rate of 15%.

The graph shows the exponential regression model for data representing a rabbit population after x years.

Which is true of the regression model?

The graph of the regression model is limited to whole-number values for y

The data in the table represents the predicted price of a gallon of milk, y, for number of years, x.

Which form of an equation was used to model the price of a gallon of milk?

y = abx
What function models the data shown on the graph?
f(x) = -2(x – 5)(x – 1)

The equation for the line of best fit is f(x) ≈ 1.8x − 5.4 for the set of values in the table.

Using the equation for the line of best fit, what is a good approximation for x when f(x) = 30?

20
Which best describes the strength of the model with an r-value of -0.93?
a strong negative correlation

The table shows the average number of hours of daylight per day for the last four months of the year.

What is the correlation coefficient for the data in the table?

-0.993

The table shows the shoe sizes of women of different ages.

Which best describes the strength of the model?

a weak positive correlation

The table shows the approximate height of an object x seconds after the object was dropped. The function h(x) = -16×2 + 100 models the data in the table.

For which value of x would this model make the least sense to use?

-2.75

The table shows a company’s profit based on the number of pounds of food produced.

Using the quadratic regression model, which is the best estimate of the profit when 350 pounds of food are produced?

\$5,300

Consider the function represented by the graph.

What is the domain of this function?

{x| x >0}
Using the equation for the line of best fit, what is a good approximation for x when f(x) = 30?
20
On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C(f)=5/9(f-32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?
the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius
What is the equation of the line in slope-intercept form that is perpendicular to the line y = x – 2 and passes through the point (-12, 10)?
y = -4/3x – 6
Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
-9

Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school.

What does the slope of the graph mean?

Tracie’s bus travels towards her home at an average speed of 1/2 mile per minute.
The graph represents a functional relationship.
Which value is an input of the function?
4
Which explains how the table can be used to predict the cost of any number of students attending the game?
The table is a partial representation of a larger data set. It can be used to generate an equation that is a complete representation of the data set.
Which is most likely the correlation coefficient for the set of data shown?
-0.21
For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?
\$2.50
Which equation can be used to find h, the number of hours Lindsay worked last week?
1/15(10h+60)=1/10(10h)
Which graph represents a function?
Sideways porabla
To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
-2/5
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Check all that apply.
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
What is the value of r, the part of the tile that Hector could install in 1 hour?
1/18
According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for \$5?
13
Which form of an equation was used to model the price of a gallon of milk?
y=ab^x
To the nearest tenth of a second, how much time would it take the penny to hit the ground?
0.6
Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?
y – 1 = 3x
How much money will she have if she doesn’t buy any packs of baseball cards?
\$20
A line of best fit for the data is represented by h = -21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?
According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground
The explicit rule for an arithmetic sequence is mc023-1.jpg What is the value of the 47th term? Round to the nearest tenth, if necessary.
-55.7

How many solutions exist for the given equation?

3(x + 10) + 6 = 3(x + 12)

infinitely many
F(x) < 0 over the intervals (-∞, -3) and
(-1.1, 0.9)
Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?
1/4(x) = x(30 + 60)