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Answer:
k = -5
Step-by-step explanation:
Hi there!
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where the two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given information:
[tex]\displaystyle -\frac{1}{5}= \displaystyle \frac{-7-k}{6-(-4)} \\\\\displaystyle -\frac{1}{5}= \displaystyle \frac{-7-k}{6+4} \\\\\displaystyle -\frac{1}{5}= \displaystyle \frac{-7-k}{10} \\\\\displaystyle -\frac{2}{10}= \displaystyle- \frac{-7-k}{10} \\\\-2=-7-k\\k=-5[/tex]
I hope this helps!