Question

Which equation represents a proportional relationship? y=−2x y=32x y = 4x + 3 y=2(x+1)

Answer 1

Equation 1:
`y = -2x`

Equation 2:
`y = 32x`

Explanation:

We are given equations in the question.

A proportionality relation can be represented in the form:

`y \propto x\\y = kx\\\text{where k is the constant of proportionality}`

Thus, equation of the form,
`y =kx` represents a proportional relationship.

Thus,
`y = -2x, y = 32x` are the equations that represent proportional relationship.

Equations,
`y = 4x + 3, y = 2(x+1) = 3x + 2` do not represent proportionality relationship.

Answer 2

Option B is correct.

y =32x represents a proportional relationship.

Explanation:

If two quantities are said to have a proportional relationship if they vary in such a way that one of the quantities is a constant multiple of the other i.e,

y = |k| y where |k| is constant proportionality.

By definition :

y =32x where k =32 is constant , represents a proportional relationship.