Linear Functions — Test Answers

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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

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 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 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 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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Which equation represents the graphed function?

negative 2 thirds x plus 2 is equal to y

2 x minus 3 is equal to y

3 halves x minus 3 is equal to y

negative 3 x plus 2 is equal to y

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 dollars per hour.

This function does not represent a direct variation because it does not represent the cost for 1 hour.

This function does not represent a direct variation because the function rule for the cost is to add 10 dollars , not multiply by a constant.

This function represents a direct variation because it has a positive, constant rate of change of 10 dollars per hour.

Whose function has the larger slope?

Marty’s with a slope of 1 third

Ethan’s with a slope of 2 fifths

Ethan’s with a slope of 1 fifth

Marty’s with a slope of 2 thirds

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

4 point 9 the fraction with numerator m and denominator s squared

19 point 6 the fraction with numerator m and denominator s squared

9 point 8 the fraction with numerator m and denominator s squared

10 point 2 the fraction with numerator m and denominator s squared

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

y is equal to negative 3 x plus 25

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

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 ?

b minus A is equal to 0

b is equal to negative A

negative b is equal to negative A

b times negative A is equal to 0

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 1 and the point 3 comma 3.

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 1 and the point 3 comma 5.

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.

Jonathan’s swimming pool holds 1,500 gallons of water. He is filling the pool with water. After 2 hours, 720 gallons of water are in the pool. After 3 hours, there are 1,080 gallons of water in the pool. Write a linear function that represents the number of gallons of water in the pool, g⁡(x) , as a function of x , the amount time in hours. Enter your answer in the box.

Answer:

g(x)=360x

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

negative 4

negative 5

The point-slope form of the equation of the line that passes through negative 4 comma negative 3 and 12 comma 1 is y minus 1 is equal to 1 fourth open paren x minus 12 close paren What is the standard form of the equation for this line?

x minus 4 y is equal to 8

x minus 4 y is equal to 2

4 x minus y is equal to 2

4 x minus y is equal to 8

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 plus y is equal to 18

5 x minus y is equal to 30

5 x plus 3 y is equal to 18

5 x minus 3 y is equal to 30

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

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

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

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 5 x minus 2 point 2 5

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

Write an equation of the line that passes through the points (−4,10) and (6,−5) in standard form. Enter your answer in the box.

Answer:

3x+2y=8

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 plus 20 point 5 0 x

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 x plus 21 point 6 0

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

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

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

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

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

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 minus 4

y is equal to 1 half x minus 7 halves

y is equal to 1 half x plus 2

y is equal to 1 half x plus 5 halves

Which graphs show functions with direct variation? Choose three correct answers.

Image with description A line graph titled Parking Garage Rates shows time in hours labeled 0 to 9 in increments of 1 on the x-axis and total cost in dollars labeled 0 to 9 in increments of 1 on the y-axis. A straight line with a positive slope passes through two labeled points, starting at 1 comma 2.4 and continuing to 5 comma 4.

Image with description A line graph titled Cost of Cinnamon shows quantity in ounces labeled 0 to 9 in increments of 1 on the x-axis and total cost in dollars labeled 0 to 9 in increments of 1 on the y-axis. A straight line with a positive slope passes through two labeled points, starting at 1 comma 0.3 and continuing to 5 comma 1.5.

Image with description A coordinate plane showing Ferry Ride Cost with Number of Persons on the x-axis and Total Cost in dollars on the y-axis with a line passing through points at (1 comma 2) and (5 comma 8).

Image with description A line graph titled Ferry Ride Cost shows number of persons labeled 0 to 9 in increments of 1 on the x-axis and total cost in dollars labeled 0 to 9 in increments of 1 on the y-axis. A straight line with a positive slope passes through two labeled points, starting at 1 comma 2 and continuing to 5 comma 8.

Image with description A line graph titled Breakfast Cost shows number of meals labeled 0 to 9 in increments of 1 on the x-axis and total cost in dollars labeled 0 to 9 in increments of 1 on the y-axis. A straight line with a positive slope passes through two labeled points, starting at 1 comma 1.2 and continuing to 5 comma 6.

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

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

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Linear Functions — Test Answers

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