Find an equation for the line that passes through the points (-5,-5) and (1,4)

The general line through (a,b) and (c,d) is

(c-a)(y-b)=(d-b)(x-a)

Here that's

(1 - - 5)(y - - 5) = (4 - -5)(x - - 5)

6(y+5)=9(x+5)

6y + 30 = 9x + 45

-15 = 9x - 6y

3x - 2y = -5

3x - 2y = -5

We could put that in slope intercept form,

2y = 3x + 5

y = (3/2) x + 5/2

y = (3/2) x + 5/2