Question

if y is directly proportional to x when x = 4 and y = -2, write an equation to model the given relationship. What is x if y = -24?

Answer 1

Direct proportion equations have the following form:

$y=kx$

Where "k" is the Constant of proportionality.

In this case you know that "y" is directly proportional to "x" and when:

$x=4;y=-2$

Having these values, you can substitute them into the equation and solve for "k":

$\begin{gathered} -2=k(4) \\ \frac{-2}{4}=k \\ k=-\frac{1}{2} \end{gathered}$

So, substituting the value of "k" into the first equation shown above, you get that the equation that models the given relationship is:

$y=-\frac{1}{2}x$

Now, to find the value of "x", when the value of "y" is -24, you must substitute this value into the equation that models the relationship and then solve for "x". Then, you get:

$\begin{gathered} -24=-\frac{1}{2}x \\ (-24)(-2)=x \\ x=48 \end{gathered}$

Therefore, the answers are:

$\begin{gathered} y=-\frac{1}{2}x \\ \\ x=48 \end{gathered}$