The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (-2, k) and (2k, 4), and m = -3,
[tex]\begin{gathered} m=\frac{4-k}{2k-(-2)} \\ -3=\frac{4-k}{2k+2} \\ -3(2k+2)=4-k \\ (-3)(2k)+(-3)(2)=4-k \\ -6k-6=4-k \\ -6k+k=4+6 \\ -5k=10 \\ k=\frac{10}{-5} \\ k=-2 \end{gathered}[/tex]