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

Option D

y = is the equation representing  proportional relationship.

Solution:

For the proportional relationship, for all values of x, must be a constant value.

Let’s check option A.

Divide both the sides by x.

For x = 1,

For x = 2,

So 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 for two values of x.

For option D

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.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.