Question

The variables x and y vary inversely. Which equation relates x and y when x = -1 and y = -9?

Answer 1

When you read the words `The variables x and y vary inversely. ` that means

\(\large\color{midnightblue}{ \rm y= }\)\(\LARGE\color{midnightblue}{ \rm \frac{k}{x} }\) where ` k ` is just the constant that relates this relation.
You have to find the k, and re-write the equation of the inverse variation with a known value of ` k ` .

You are given that ` x=-1 ` and ` y = -9 ` plug the given information into the equation of the inverse variation (that I wrote above in dark blue letters)

\(\large\color{midnightblue}{ \rm (-9)= }\)\(\LARGE\color{midnightblue}{ \rm \frac{k}{(-1)} }\) Now you are to solve for ` k ` . Multiply both sides by -1, and you get

\(\large\color{midnightblue}{ \rm 9= k }\) Hence, the equation of your inverse variation is, \(\large\color{midnightblue}{ \rm y= }\)\(\LARGE\color{midnightblue}{ \rm \frac{9}{x} }\)