The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁,y₁) - point
[tex](3,-2) \\
x_1=3 \\ y_1=-2 \\ \\
(8,2) \\
x_2=8 \\ y_2=2 \\ \\ \hbox{the slope:} \\
m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-2)}{8-3}=\frac{2+2}{5}=\frac{4}{5} \\ \\ \hbox{the point-slope form:} \\
y-y_1=m(x-x_1) \\
y-(-2)=\frac{4}{5}(x-3) \\
\boxed{y+2=\frac{4}{5}(x-3)}[/tex]
[tex]\hbox{the standard form:} \\
y+2=\frac{4}{5}(x-3) \\
y+2=\frac{4}{5}x-\frac{12}{5} \\
-\frac{4}{5}x+y=-\frac{12}{5}-2 \ \ \ |\times 5 \\
-4x+5y=-12-10 \\
\boxed{-4x+5y=-22}[/tex]
The answer is D.