Question

Which equation represents a proportional relationship? A. y = x + 1 3 y=x+13 B. y = 1 − 1 3 x y=1-13x C. y = 3 x + 1 3 y=3x+13 D. y = 1 3 x

Answer 1

y=1/3

Explanation:

I took the test and got it right.

Answer 2

Option D.
`y=(1)/(3)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
`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

case A) we have

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

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

`y=0+(1)/(3)=(1)/(3)`

so

The line not passes through the origin

therefore

The equation A not represent a proportional relationship

case B) we have

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

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

`y=1-(1)/(3)(0)=1`

so

The line not passes through the origin

therefore

The equation B not represent a proportional relationship

case C) we have

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

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

`y=3(0)+(1)/(3)=(1)/(3)`

so

The line not passes through the origin

therefore

The equation C not represent a proportional relationship

case D) we have

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

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

`y=(1)/(3)(0)=0`

so

The line passes through the origin

therefore

The equation D represent a proportional relationship