Question

Given that x = -18 and y = -9 in a direct variation, what is the equation that relates the variables x and y?

a) y = 2x
b) y = -x
c) y = -2x
d) y = x/2

Answer 1

The equation that relates the variables x and y in direct variation is y = -2x.

Step-by-step explanation:

The equation that relates the variables x and y in direct variation is y = -2x.

Direct variation is a mathematical relationship between two variables in which one variable is a constant multiple of the other. In this case, since x and y vary directly, the equation is in the form y = kx, where k is the constant of variation.

Given that x = -18 and y = -9, we can substitute these values into the equation y = kx and solve for k. Plugging in the values, we have -9 = k(-18). Solving for k, we get k = -9/(-18) = 1/2. So the equation that relates x and y is y = (1/2)x. Multiplying both sides of the equation by 2, we get y = -2x.