AnswersKCPS Algebra I 2027Linear Functions

Linear Functions — Test Answers

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1
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What is the rate of change of the amount earned with respect to hours worked for this function?

A
1 thirteenth hours per dollar
B
2 fifths hours per dollar
C
3 dollars per hour
D
13 dollars per hour
2
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Which steps should be used to graph the equation? y minus 4 is equal to 1 third times x plus 2

A
1. Plot the point negative 2 comma 4 . 2. From that point, count left 1 unit and down 3 units and plot a second point. 3. Draw a line through the two points.
B
1. Plot the point 2 comma 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.
C
1. Plot the point 2 comma 4 . 2. From that point, count left 1 unit and down 3 units and plot a second point. 3. Draw a line through the two points.
D
1. Plot the point negative 2 comma 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.
3

What is the slope of the function?

A
negative 3
B
3
C
4
D
negative 2
4

The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool?

A
The height of the water decreases 2 inches per minute.
B
The height of the water will be 2 inches when the pool is filled.
C
The height of the water increases 2 inches per minute.
D
The height of the water was 2 inches before any water was added.
5

What is the constant of variation for the subscription cost based on the number of weeks?

A
1 point 5 0 dollars
B
15 point 0 0 dollars
C
7 point 5 0 dollars
D
30 point 0 0 dollars
6

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

A
1 point 50 dollars per book
B
0 point 50 dollars per book
C
0 point 67 dollars per book
D
1 point 07 dollars per book
7

What is the slope of the line?

A
3
B
negative 3
C
1 third
D
negative 1 third
8

Which of these values could be the slope of the line? Choose two correct answers.

A
negative 2
B
0
C
negative 8 fifths
D
3
E
7 fourths
9

Which equation represents the graphed function?

A
negative 2 thirds x plus 2 is equal to y
B
3 halves x minus 3 is equal to y
C
2 x minus 3 is equal to y
D
negative 3 x plus 2 is equal to y
10

Line cap c cap d passes through points C 3 comma negative 5 and D 6 comma 0 What is the equation of line cap c cap d in standard form?

A
5 x plus 3 y is equal to 18
B
5 x plus y is equal to 18
C
5 x minus 3 y is equal to 30
D
5 x minus y is equal to 30
11

Which equation represents the line that passes through negative 6 comma 7 and negative 3 comma 6 ?

A
y is equal to negative 1 third x plus 9
B
y is equal to negative 3 x minus 11 y
C
y is equal to negative 1 third x plus 5
D
y is equal to negative 3 x plus 25
12

On a number line, a number, b , is located the same distance from 0 as another number, A , but in the opposite direction. The number b varies directly with the number A For example b is equal to 2 and 3 fourths when A is equal to negative 2 and 3 fourths Which equation represents this direct variation between A and b ?

A
b minus A is equal to 0
B
b is equal to negative A
C
negative b is equal to negative A
D
b times negative A is equal to 0
13

A store offers packing and mailing services to customers. The cost of shipping a box is a combination of a flat packing fee of 5 dollars and an amount based on the weight in pounds of the box, 2 point 2 5 dollars per pound. Which equation represents the shipping cost as a function of x , the weight in pounds?

A
f of x is equal to 2 point 2 5 x minus 5
B
f of x is equal to 5 x plus 2 point 2 5
C
f of x is equal to 5 x minus 2 point 2 5
D
f of x is equal to 2 point 2 5 x plus 5
14

Which graph represents a function with direct variation?

A
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a positive slope passes through approximately the points negative 3 comma negative 4, 0 comma 1, 1 comma 2.5, and 3 comma 5.
B
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a negative slope passes through approximately the points negative 4 comma 5, 0 comma 1, 1 comma 0, and 5 comma negative 4.
C
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a negative slope passes through approximately the points negative 4 comma 2, 0 comma 0, 2 comma negative 1, and 4 comma negative 2.
D
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A straight line with a positive slope passes through approximately the points negative 5 comma negative 3.5, 0 comma negative 2, 3 comma negative 1, and 5 comma negative 0.3.
15

Alejandra correctly wrote the equation y minus 3 is equal to 1 fifth times open paren x minus 10 close paren 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?

A
y minus 3 is equal to 1 fifth times open paren x minus 2 close paren
B
y minus 2 is equal to 1 fifth times open paren x minus 10 close paren
C
y minus 6 is equal to 2 times open paren x minus 10 close paren
D
y minus 3 is equal to 2 times open paren x minus 10 close paren
16

Which equation represents a line that passes through 2 comma negative 1 half and has a slope of 3 ?

A
y minus 2 is equal to 3 times open paren x plus 1 half close paren
B
y plus 1 half is equal to 2 times open paren x minus 3 close paren
C
y minus 3 is equal to 2 times open paren x plus 1 half close paren
D
y plus 1 half is equal to 3 times open paren x minus 2 close paren
17

Which is the graph of the equation y minus 1 is equal to 2 thirds times x minus 3 ?

A
Image with description A coordinate plane has both x and y axes labeled from negative 10 to 10. A straight line is plotted that passes through the point negative 3 comma 1 and the point 3 comma 5.
B
Image with description A coordinate plane has both x and y axes labeled from negative 10 to 10. A straight line is plotted that passes through the point negative 3 comma negative 1 and the point 3 comma 3.
C
Image with description A coordinate plane has both x and y axes labeled from negative 10 to 10. A straight line is plotted that passes through the point negative 3 comma negative 3 and the point 3 comma 1.
D
Image with description A coordinate plane with the x-axis labeled from negative 10 to 10 and the y-axis labeled from negative 10 to 10. A straight line is plotted that passes through the point negative 3 comma negative 5 and the point 3 comma negative 1.
18

What is the slope of the line represented by the equation f of t is equal to 2 t minus 6 ?

A
The slope is 2 and the y -intercept is negative 6 .
B
The slope is 2 and the y -intercept is 6 .
C
The slope is negative 6 and the y -intercept is 2 .
D
The slope is 6 and the y -intercept is 2 .
19

The point-slope form of the equation of the line that passes through negative 9 comma negative 2 and 1 comma 3 is y minus 3 is equal to 1 half open paren x minus 1 close paren What is the slope-intercept form of the equation for this line?

A
y is equal to 1 half x plus 2
B
y is equal to 1 half x plus 5 halves
C
y is equal to 1 half x minus 7 halves
D
y is equal to 1 half x minus 4
20

Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. Which best describes this function?

A
It is linear because the graph decreases over time.
B
It is nonlinear because linear functions increase or decrease at the same rate.
C
It is linear because there is both an independent and a dependent variable.
D
It is nonlinear because linear functions are increasing functions.

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