Answer
$11x+y=-52$
Work Step by Step
Using $y-y_1=\dfrac{y_1-y_2}{x_1-x_2}(x-x_1)$ or the Two-Point Form, the equation of the line passing through $(
-5,3
)$ and $(
-4,-8
)$ is
\begin{array}{l}
y-3=\dfrac{3-(-8)}{-5-(-4)}(x-(-5))
\\\\
y-3=\dfrac{3+8}{-5+4}(x+5)
\\\\
y-3=\dfrac{11}{-1}(x+5)
\\\\
y-3=-11(x+5)
\\\\
y-3=-11x-55
\\\\
11x+y=-55+3
\\\\
11x+y=-52
.\end{array}