Question

Find the constant of variation k for the direct variation. Then write an equation for the inverse variation. Y= 4.5 when x= 3

Answer 1

The constant for variation is k = 3/2 and the equation for the inverse is y = 2/3x

In order to find this, we need to start with the base equation for direct variation. We can then plug in the values and solve for k.

y = kx

4.5 = k(3)

1.5 = k

Now we can model the equation as y = 3/2x. We can then find the inverse by switching the x and y and solving for the new y.

y = 3/2x ----> Switch

x = 3/2y -----> Multiply by 2/3

2/3x = y