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Linear Functions — Test Answers

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

1 thirteenth hours per dollar

13 dollars per hour

2 fifths hours per dollar

3 dollars per hour

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

y is equal to negative 3 x minus 11 y

y is equal to negative 1 third x plus 5

y is equal to negative 1 third x plus 9

y is equal to negative 3 x plus 25

A ramp with a constant incline is made to connect a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?

1 third inch up per foot across

3 inches up per foot across

2 inches up per foot across

1 half inch up per foot across

What is the y -intercept of the function f of x is equal to 4 minus 5 x ?

negative 5

negative 4

A line contains points cap m of 1 comma 3 and cap n of 5 comma 0 What is the slope of line segment MN ?

negative 4 thirds

negative 3 fourths

4 thirds

3 fourths

Which graph represents a function with direct variation?

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.

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.

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.

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.

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

y minus 2 is equal to 3 times open paren x plus 1 half close paren

y minus 3 is equal to 2 times open paren x plus 1 half close paren

y plus 1 half is equal to 3 times open paren x minus 2 close paren

y plus 1 half is equal to 2 times open paren x minus 3 close paren

Tickets to a basketball game can be ordered online for a set price per ticket plus a 5 dollars and 50 cents service fee. The total cost in dollars for ordering 5 tickets is 108 dollars Which linear function represents c , the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).

c of x is equal to 5 point 5 0 x plus 21 point 6 0

c of x is equal to 5 point 5 0 plus 21 point 6 0 x

c of x is equal to 5 point 5 0 x plus 20 point 5 0

c of x is equal to 5 point 5 0 plus 20 point 5 0 x

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?

y is equal to 1 half x plus 5 halves

y is equal to 1 half x minus 7 halves

y is equal to 1 half x minus 4

y is equal to 1 half x plus 2

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?

f of x is equal to 2 point 2 5 x plus 5

f of x is equal to 5 x minus 2 point 2 5

f of x is equal to 5 x plus 2 point 2 5

f of x is equal to 2 point 2 5 x minus 5

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

The slope is 2 and the y -intercept is negative 6 .

The slope is 2 and the y -intercept is 6 .

The slope is negative 6 and the y -intercept is 2 .

The slope is 6 and the y -intercept is 2 .

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

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.

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.

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.

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.

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 ?

negative b is equal to negative A

b is equal to negative A

b minus A is equal to 0

b times negative A is equal to 0

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?

It is nonlinear because linear functions are increasing functions.

It is nonlinear because linear functions increase or decrease at the same rate.

It is linear because there is both an independent and a dependent variable.

It is linear because the graph decreases over time.

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?

5 x minus 3 y is equal to 30

5 x plus y is equal to 18

5 x minus y is equal to 30

5 x plus 3 y is equal to 18

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?

y minus 6 is equal to 2 times open paren x minus 10 close paren

y minus 3 is equal to 1 fifth times open paren x minus 2 close paren

y minus 2 is equal to 1 fifth times open paren x minus 10 close paren

y minus 3 is equal to 2 times open paren x minus 10 close paren

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

1 point 07 dollars per book

1 point 50 dollars per book

0 point 67 dollars per book

0 point 50 dollars per book

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

7 point 5 0 dollars

1 point 5 0 dollars

15 point 0 0 dollars

30 point 0 0 dollars

Which equation represents the graphed function?

2 x minus 3 is equal to y

negative 2 thirds x plus 2 is equal to y

negative 3 x plus 2 is equal to y

3 halves x minus 3 is equal to y

Which steps should be used to graph the equation? y minus 4 is equal to 1 third times x plus 2

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.

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.

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.

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.

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