Option D
Answer:
y = [tex]\frac{1}{3}[/tex] is the equation representing proportional relationship.
Solution:
For the proportional relationship, for all values of x, [tex]\frac{y}{x}[/tex] must be a constant value.
Let’s check option A.
[tex]y=x+\frac{1}{3}[/tex]
Divide both the sides by x.
[tex]\frac{y}{x}=1+\frac{1}{3 x}[/tex]
For x = 1,
[tex]\frac{y}{x}=1+\frac{1}{3 \times 1}=\frac{4}{3}[/tex]
For x = 2,
[tex]\frac{y}{x}=1+\frac{1}{3 \times 2}=6[/tex]
So [tex]\frac{y}{x}[/tex] 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 [tex]\frac{y}{x}[/tex] for two values of x.
For option D
[tex]y=\frac{1}{3} x[/tex]
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.
