Question

Suppose y varies directly with x when x is -2 y is 10 write the equation that relates x and y

Answer 1

The form of the equation of the direct proportional is

$y=kx$

k is the constant of variation

We can find it from the initial values of x and y

Since at x = -2 y = 10, then

Substitute x by -2 and y by 10 to find k

$\begin{gathered} x=-2,y=10 \\ 10=k(-2) \\ 10=-2k \end{gathered}$

Divide both sides by -2 to find k

$\begin{gathered} \frac{10}{(-2)}=\frac{-2k}{(-2)} \\ -5=k \end{gathered}$

The value of k is -5

Then the equation is

$y=-5x$