Question

which equation reprents a propotional relationship? 1/4 x + y = 10 y = 3x + 7 y = 1/3x + 1 y = 1/4 x

Answer 1

`y=(1)/(4)x`

Explanation:

we know that

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

case 1) we have

`(1)/(4)x+y=10`

Remember that

In a proportional relationship the line passes through the origin

That means ----> For x=0, the value of y also must be zero

For x=0

`(1)/(4)(0)+y=10\\\\y=10`

therefore

The equation not represent a a proportional relationship

case 2) we have

`y=3x+7`

This is the equation of the line in slope intercept form

The y-intercept is b=7 ----> is not equal to zero

therefore

The equation not represent a a proportional relationship

case 3) we have

`y=(1)/(3)x+1`

This is the equation of the line in slope intercept form

The y-intercept is b=1 ----> is not equal to zero

therefore

The equation not represent a a proportional relationship

case 4) we have

`y=(1)/(4)x`

This is a linear equation expressed in the form
`y=kx`

where

The constant of proportionality k or slope is equal to

`k=(1)/(4)`

For x=0, y=0

therefore

The equation represent a a proportional relationship