Answer
$2x+y=8$
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 $(
5,-2
)$ and $(
-3,14
)$ is
\begin{array}{l}\require{cancel}
y-(-2)=\dfrac{-2-14}{5-(-3)}(x-5)
\\\\
y+2=\dfrac{-2-14}{5+3}(x-5)
\\\\
y+2=\dfrac{-16}{8}(x-5)
\\\\
y+2=-2(x-5)
\\\\
y+2=-2x+10
\\\\
2x+y=10-2
\\\\
2x+y=8
.\end{array}
