6y=-12x

Question

Part 1: Determine whether the equation represents a direct variation.

Part 2: If it does find the constant of variation

Answer 1

Part 1: Determine whether the equation represents a direct variation.

An equation represents a direct variation if it can be expressed in the form y = kx, where k is a non-zero constant called the constant of variation. The equation given is 6y = -12x. To determine if this is a direct variation, we need to solve for y in terms of x.

To do this, divide both sides of the equation by 6:

6y/6 = (-12x)/6
y = -2x

Now the equation is in the form y = kx, where k is -2.

Since the equation can be rewritten in the direct variation form (y = kx), it does represent a direct variation.

Part 2: Find the constant of variation.

The constant of variation k is the coefficient of x in the direct variation equation y = kx. From the equation y = -2x that we derived, the constant of variation is k = -2.