Question

Which equation represents a proportional relationship?

Answer 1

Option D

Answer:

y = $\frac{1}{3}$ is the equation representing  proportional relationship.

Solution:

For the proportional relationship, for all values of x, $\frac{y}{x}$ must be a constant value.

Let’s check option A.

$y=x+\frac{1}{3}$

Divide both the sides by x.

$\frac{y}{x}=1+\frac{1}{3 x}$

For x = 1,

$\frac{y}{x}=1+\frac{1}{3 \times 1}=\frac{4}{3}$

For x = 2,

$\frac{y}{x}=1+\frac{1}{3 \times 2}=6$

So $\frac{y}{x}$ 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 $\frac{y}{x}$ for two values of x.

For option D

$y=\frac{1}{3} x$

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.