Question

Which equation represents a proportional relationship?

A.y = x + 1/3
B.y = 1 − 1/3 x
C. y = 3 x + 1/3
D.y = 1/3 x

Answer 1

Option D

Answer:

y =
`(1)/(3)` is the equation representing proportional relationship.

Solution:

For the proportional relationship, for all values of x,
`(y)/(x)` must be a constant value.

Let’s check option A.

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

Divide both the sides by x.

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

For x = 1,

`(y)/(x)=1+(1)/(3 * 1)=(4)/(3)`

For x = 2,

`(y)/(x)=1+(1)/(3 * 2)=6`

So
`(y)/(x)` is different for x = 1 and x = 2.

So option A do not represent proportional relationship.

Similarly for option B and C also there is constant term in the equation.

So option B and C will also have different values of
`(y)/(x)` for two values of x.

For option D

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

So for all value of x in above case y/x will be 1/3 .hence D is correct option , that is y = (1/3)x is the equation represents proportional relationship.