Question

1. Find the value of k so that the line that passes through the points (-2, k) and (2k, 4) has a slope of -3. (2 points) k =

Answer 1

The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:

`m=(y_2-y_1)/(x_2-x_1)`

Replacing with points (-2, k) and (2k, 4), and m = -3,

`\begin{gathered} m=(4-k)/(2k-(-2)) \\ -3=(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=(10)/(-5) \\ k=-2 \end{gathered}`