Write an inverse variation equation

The problem reads: "The variables x and y vary inversely, and y=7 when x=4. Write an equation that relates x and y, and then find y when x=-2."
Thanks for your help!

First write the general equation for inverse variation:

y = a/x where a is the constant of variation, and y is said to vary inversely with x.
Also note that a cannot equal zero.

Next substitute 7 for y and 4 for x:

7 = a/4

Now solve for a

a = 28

And so the inverse variation equation is

y = 28/x

For the second part of the question you plug in -2 for x and solve

y =28/-2

y = -14

Therefore when x=-2, y=-14

:)

y=k/x