Mathematics, 23.11.2020 05:40 shafferakr6

Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0), and (1, 4).

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Answer from: payshencec21

A line passing through the points (-1,-4),(0,0) and (1,4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

Part 1) A line passing through the points (-4,0) and (0,-2)

This line not represent a direct variation, because the line not passes through the origin.

Part 2) A line passing through the points (-5,4) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 3) A line passing through the points (-4,-6) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 4) A line passing through the points (-1,-4),(0,0) and (1,4)

The line passes through the origin

Find out the value of k

k=y/x

For the point (-1,-4)

substitute

k=-4/-1=4

For the point (1,4)

substitute

k=4/1=4

The linear equation is y=4x

This line represent a direct variation

Answer from: OliTepley8032

A line passing through the points (-1,-4),(0,0) and (1,4)

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

Part 1) A line passing through the points (-4,0) and (0,-2)

This line not represent a direct variation, because the line not passes through the origin.

Part 2) A line passing through the points (-5,4) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 3) A line passing through the points (-4,-6) and (0,3)

This line not represent a direct variation, because the line not passes through the origin.

Part 4) A line passing through the points (-1,-4),(0,0) and (1,4)

The line passes through the origin

Find out the value of k

k=y/x

For the point (-1,-4)

substitute

k=-4/-1

k=4

For the point (1,4)

substitute

k=4/1

k=4

The linear equation is

y=4x

This line represent a direct variation

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