Question

Which equation represents a proportional relationship?

A. y=−3x+2

B. y=12x

C. y = 3x

D. y=2(x+13)

Answer 1

`y=12x`

`y=3x`

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 of the line m, and the line passes trough the origin

so

case A)
`y=-3x+2`

Is a linear equation but does not passes trough the origin

case B)
`y=12x`

Is a linear equation and passes trough the origin-----> represent a proportional relationship

case C)
`y=3x`

Is a linear equation and passes trough the origin-----> represent a proportional relationship

case D)
`y=2(x+13)`

Is a linear equation but does not passes trough the origin

Answer 2

As written here, both choices B and C represent proportional relationships:

... B. y = 12x

... C. y = 3x

_____

One key to a proportional relationship is that when one variable is zero, so is the other. This will not be the case for selections A and D.