Answer
$x+2y=8$
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 $(
6,1
)$ and $(
-2,5
)$ is
\begin{array}{l}\require{cancel}
y-1=\dfrac{1-5}{6-(-2)}(x-6)
\\\\
y-1=\dfrac{1-5}{6+2}(x-6)
\\\\
y-1=\dfrac{-4}{8}(x-6)
\\\\
y-1=-\dfrac{1}{2}(x-6)
\\\\
2(y-1)=-1(x-6)
\\\\
2y-2=-x+6
\\\\
x+2y=6+2
\\\\
x+2y=8
.\end{array}