Answer
$2x-3y=-19$
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 of linear equations, the equation of the line passing through $(
-2,5
)$ and $(
-8,1
)$ is
\begin{array}{l}\require{cancel}
y-5=\dfrac{5-1}{-2-(-8)}(x-(-2))
\\\\
y-5=\dfrac{5-1}{-2+8}(x+2)
\\\\
y-5=\dfrac{4}{6}(x+2)
\\\\
y-5=\dfrac{2}{3}(x+2)
\\\\
3(y-5)=2(x+2)
\\\\
3y-15=2x+4
\\\\
-2x+3y=4+15
\\\\
-2x+3y=19
\\\\
2x-3y=-19
.\end{array}