Answer:
k = - 37
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- k, - 5) and (x₂, y₂ ) = (- 3, k+2)
m = [tex]\frac{k+2+5}{-3+k}[/tex], that is
[tex]\frac{k+7}{-3+k}[/tex] = [tex]\frac{3}{4}[/tex] ( cross- multiply )
4(k + 7) = 3(- 3 + k) ← distribute both parenthesis
4k + 28 = - 9 + 3k ( subtract 3k from both sides )
k + 28 = - 9 ( subtract 28 from both sides )
k = - 37
