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.
6y=-12x
Part 1: Determine whether the equation represents a direct variation.
Part 2: If it does find the constant of variation
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