Question

Which of the equations below represent proportional relationships? If the relationship is proportional, identify the constant of proportionality. If the relationship is not proportional, explain why.

a) (y = 2x)
b) (y = frac(1)(3)x)
c) (y = x^2)
d) (y = frac(4)(5)x)

Answer 1

The equation that represents a proportional relationship is (a) y = 2x.

Step-by-step explanation:

The equation that represents a proportional relationship is (a) y = 2x. This equation shows that for every increase of 1 in x, y increases by 2. The constant of proportionality in this equation is 2.

The equation in option (b) y = frac(1)(3)x is also proportional, with a constant of proportionality of 1/3. However, the equation in option (c) y = x^2 is quadratic, not proportional. In a quadratic relationship, the values of y are not directly proportional to x. Similarly, the equation in option (d) y = frac(4)(5)x is not proportional, as the values of y are not directly proportional to x.