Question

Write an appropriate direct variation equation if y = 30 when x = -10.

If y varies inversely as x, and y = 10 when x = 7, find y for the x-value of 10.

If y varies directly as x, and y = 25 as x = 5, find y for the x-value 7.

Answer 1

The general equation of direct variation is

\(y = kx\)

where \(k\) is a constant called the "constant of proportionality."

You know one point that satisfies the equation, so replace x and y in the general equation with the given values and solve for k.

Once you know k, rewrite the general equation with the value you found for k instead of the variable k. That is your direct variation equation.

For inverse variation, the general equation is

\(y = \dfrac{x}{k} \)

where \(k\) is a constant.

Follow the same procedure as above with a known point to find k.
Then write the equation for the inverse variation using your value of k.