Answer:
k= -14
Step-by-step explanation:
[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]
[tex] \frac{5}{3} = \frac{7 - (3 - k)}{k + 3 - ( - 5)} [/tex]
[tex] \frac{5}{3} = \frac{7 - 3 + k}{k + 3 + 5} [/tex]
[tex] \frac{5}{3} = \frac{4 + k}{k + 8} [/tex]
Cross multiply:
3(4 +k)= 5(k +8)
Expand:
12 +3k= 5k +40
Bring k terms to one side, constant to the other:
5k -3k= 12 -40
Simplify:
2k= -28
Divide both sides by 2:
k= -14
