Lets first find the slope:
(y₂-y₁)=m(x₂-x₁)
(-9-(-3)) = m(-4-6)
-6 = m(-10)
Isolate m:
[tex] \frac{-6}{-10} [/tex] = [tex] \frac{m(-10)}{-10} [/tex]
-10 and -10 cancels out
[tex] \frac{-6}{-10} [/tex] = m
[tex] \frac{3}{5} [/tex] = m
Now we know the slope, which is [tex] \frac{3}{5} [/tex]
The equations is
y = mx + c
Take any two coordinates from the given above
Im taking (6,-3)
Plug in those coordinates and the slope to the formula
-3 = [tex] \frac{3}{5} [/tex](6) + c
-3 = [tex] \frac{18}{5} [/tex] + c
Isolate c
-3 - [tex] \frac{18}{5} [/tex] = c
[tex]- \frac{33}{5} [/tex] = c
which gives us:
-6.6 = c
Now plug in the slope and c in the equation:
y = [tex] \frac{3}{5} [/tex]x+ (-6.6)
or
y = [tex] \frac{3}{5} [/tex]x +(-[tex] \frac{33}{5} [/tex])
