Hello from MrBillDoesMath!
Answer: y - (-8) = (-14/11) (x -7) or y + 8 = (-14/11) (x-7)
Steps:
Let's call point (7, -8) (x1,y1) and point (-4,6) (x2,y2). The point slope equation of a line through (x1, y1) is
y- y1 = m(x-x1)
where "m" is the slope of the non-vertical line. Recall that m is rise/run or
m = (y2- y1)/(x2-x1).
In our case
m = (6 - (-8))/( -4 - 7) = (6 + 8)/ (-11) = - 14/11
The point-slope equation becomes
y - (-8) = (-14/11) (x -7)
This can be rewritten as y + 8 = (-14/11) (x-7)
As a final check, you should verify that this equation passes through the original points using substitution!
Regards, MrB.