Question

For the equation y = 4x², which two variables are directly proportional to each other?

a) y and x
b) x and 4
c) y and 4x
d) x² and y

Answer 1

For the equation y = 4x², the two variables that are directly proportional to each other are x² and y, as y is proportional to the square of x.

Step-by-step explanation:

The equation given is y = 4x². In this equation, we can see that y is dependent on the square of x. Two variables are directly proportional to each other if a change in one variable causes a proportional change in the other. In a direct proportionality y = kx, where k is the proportionality constant and does not involve any powers greater than one. Since x² is x raised to the power of two, y is not directly proportional to x itself, but rather to x². Hence, the correct answer is d) x² and y, as y equals 4 times the square of x, and thus the square of x (x²) and y are directly proportional to each other.