Lets find the slope first.
Slope is change in y's by change in x's.
Change in y's = -8 -2 = -10
Change in x's = -8 -8 = -16
Slope = -10/-16 = 5/8
The slope intercept form is:
y = mx + b
Where
m is slope
b is y intercept
We now have:
[tex]y=\frac{5}{8}x+b[/tex]We can plug in any point and find b. Let's put (8,2), so :
[tex]\begin{gathered} y=\frac{5}{8}x+b \\ 2=\frac{5}{8}(8)+b \\ 2=5+b \\ b=2-5 \\ b=-3 \end{gathered}[/tex]Final equation:
[tex]y=\frac{5}{8}x-3[/tex]