Answer:
k = -4 or 2
Step-by-step explanation:
For the lines to be parallel, the lines would need to be the same slope. This means to find the slope of each we would take the difference of the rise over the run.
[tex]\frac{1-3}{-2-k}=\frac{-2}{-2-k}[/tex]
and
[tex]\frac{0-k}{1-5}=\frac{-k}{-4}[/tex]
To find K, set them equal.
[tex]\frac{-2}{-2-k} = \frac{-k}{-4}\\-k(-2-k) = -2*-4\\2k+k^2=8\\k^2+2k-8=0[/tex]
Factor the quadratic and solve for K.
[tex](k+4)(k-2)=0[/tex]
k+4=0 so k=-4
k-2=0 so k=2
