AnswersWI-Mathematics Grade 8 ASlope-Intercept Form

Slope-Intercept Form Answers

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Eric earns a weekly salary and a commission on each item that he sells. The equation y = 10x + 50 represents the amount of money that Eric earns weekly. Bailey earns a greater weekly salary than Eric but the same commission rate. Which graph could represent the amount of money that Bailey earns weekly, y, based on the number of items sold, x?

A
A graph titled Bailey's Weekly Earnings has items sold on the x-axis and total earned on the y-axis. A line goes through points (0, 75), (5, 125), (10, 175).
Option A
B
A graph titled Bailey's Weekly Earnings has items sold on the x-axis and total earned on the y-axis. A line goes through points (0, 50), (1, 75), (2, 100).
Option B
C
A graph titled Bailey's Weekly Earnings has items sold on the x-axis and total earned on the y-axis. A line goes through points (0, 75), (1, 100), (2, 125).
Option C
D
A graph titled Bailey's Weekly Earnings has items sold on the x-axis and total earned on the y-axis. A line goes through points (0, 50), (5, 100), (10, 150).
Option D
2
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The equation represents the gallons of gasoline that remain in Michelle’s car after she drives x miles. Which graph represents this equation?

Question illustration
A
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (40, 8).
Option A
B
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 11) and (80, 8).
Option B
C
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 12) and (125, 6).
Option C
D
A graph titled Driving has total miles traveled on the x-axis and gallons of gasoline on the y-axis. A line goes through points (0, 10) and (150, 0).
Option D
3

The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?

A
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
B
Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
C
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
D
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
4

Adriana writes the equation y = 2x + 4 to represent a line on a graph. Henry writes an equation that has a y-intercept that is 1 unit lower on the graph but has the same slope as Adriana’s line. Which is Henry’s equation?

A
y = x + 4
B
y = 3x + 4
C
y = 2x + 3
D
y = 2x + 5
5

Which statements accurately describe how to determine the y-intercept and the slope from the graph below?

Question illustration
A
To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation .
Option A
B
To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation .
Option B
C
To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation .
Option C
D
To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation .
Option D
6

Carey correctly graphs a linear function. The slope of the function is –1. The y-intercept is 3. Which is Carey’s graph?

A
On a coordinate plane, a line goes through points (0, 3) and (3, 0).
Option A
B
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Option B
C
On a coordinate plane, a line goes through points (0, negative 1) and (1, 2).
Option C
D
On a coordinate plane, a line goes through points (negative 1, 2) and (0, negative 1).
Option D
7

What is the slope, m, and y-intercept for the line that is plotted on the grid below?

Question illustration
A
m = , (0, –2)
Option A
B
m = , (0, 4)
Option B
C
m = 2, (0, –2)
D
m = 2, (0, 4)
8

Kelsey graphed the equation y = 3x + 1 as shown below.Which describes Kelsey’s error?

Question illustration
A
Kelsey graphed the y-intercept on the x-axis.
B
Kelsey graphed –3 instead of 3 as the y-intercept.
C
Kelsey graphed the slope as up 1 right 1 instead of up 1 left 1.
D
Kelsey graphed the slope as the y-intercept and the y-intercept as the slope.
9

A teacher has a 2-gallon (32-cup) container of juice. She gives each student cup of juice. Which equation represents the amount of juice that remains, y, after x students are served?

Question illustration
A
y = 32 x minus one-half
Option A
B
y = one-half x minus 32
Option B
C
y = negative one-half x + 32
Option C
D
y = negative 32 x + one-half
Option D
10

Samantha’s parents give her $10 per week. For each chore that she does not complete, she must repay her parents $1. Which graph models Samantha’s allowance?

A
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (0, 10) and (1, 9).
Option A
B
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (0, 10) and (2, 12).
Option B
C
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (1, 6) and (1.5, 16).
Option C
D
A graph titled Samantha's Allowance has chores not completed on the x-axis and amount earned on the y-axis. A line goes through points (0, 10) and (1, 0).
Option D
11

Carey correctly graphs a linear function. The slope of the function is –1. The y-intercept is 3. Which is Carey’s graph?

A
On a coordinate plane, a line goes through points (0, 3) and (3, 0).
Option A
B
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 3).
Option B
C
On a coordinate plane, a line goes through points (0, negative 1) and (1, 2).
Option C
D
On a coordinate plane, a line goes through points (negative 1, 2) and (0, negative 1).
Option D
12

The estimated total cost, y, of a child’s toy is partially based on the number of batteries used, x. The cost of one battery is $0.75. The toy itself costs $12. Which equation represents the situation?

A
y = 12x + 0.75
B
y = 0.75x + 12
C
y = 12x – 0.75
D
y = 0.75x – 12
13

Adriana writes the equation y = 2x + 4 to represent a line on a graph. Henry writes an equation that has a y-intercept that is 1 unit lower on the graph but has the same slope as Adriana’s line. Which is Henry’s equation?

A
y = x + 4
B
y = 3x + 4
C
y = 2x + 3
D
y = 2x + 5
14

A sand dune stands 5 feet above sea level. The hill is eroding at a rate of 1 foot per 20 years. Let y represent the height of the sand dune after x years. Which equation represents the situation?

A
y = negative StartFraction 1 Over 20 EndFraction x minus 5
Option A
B
y = negative StartFraction 1 Over 20 EndFraction x + 5
Option B
C
y = negative 20 x minus 5
Option C
D
y = negative 20 x + 5
Option D
15

What is the slope and equation of a line through the points (0, 9) and (3, 0)?

A
; y = –3x + 9
Option A
B
; y = –3x + 3
Option B
C
;
Option C
D
;
Option D
16

Which is the graph of the linear function that is represented by the equation ?

Question illustration
A
On a coordinate plane, a line goes through points (negative 1, 0) and (0, 2).
Option A
B
On a coordinate plane, a line goes through points (negative 2, 0) and (0, 1).
Option B
C
On a coordinate plane, a line goes through points (0, negative 2) and (4, 0).
Option C
D
On a coordinate plane, a line goes through points (0, negative 2) and (1, 0).
Option D
17

At breakfast, a restaurant charges $2 for the first cup of orange juice and then $1 for each refill. Which graph represents this situation?

A
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 1) and (1, 3).
Option A
B
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 1) and (1, 2).
Option B
C
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 2) and (1, 4).
Option C
D
A graph titled Orange Juice has number of refills on the x-axis and total cost on the y-axis. A line goes through points (0, 2) and (1, 3).
Option D

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