Direct proportion equations have the following form:
[tex]y=kx[/tex]
Where "k" is the Constant of proportionality.
In this case you know that "y" is directly proportional to "x" and when:
[tex]x=4;y=-2[/tex]
Having these values, you can substitute them into the equation and solve for "k":
[tex]\begin{gathered} -2=k(4) \\ \frac{-2}{4}=k \\ k=-\frac{1}{2} \end{gathered}[/tex]
So, substituting the value of "k" into the first equation shown above, you get that the equation that models the given relationship is:
[tex]y=-\frac{1}{2}x[/tex]
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:
[tex]\begin{gathered} -24=-\frac{1}{2}x \\ (-24)(-2)=x \\ x=48 \end{gathered}[/tex]
Therefore, the answers are:
[tex]\begin{gathered} y=-\frac{1}{2}x \\ \\ x=48 \end{gathered}[/tex]
