Question

What is the equation in point-slope form of a line that passes through the points (7, −8) and (−4, 6) ?

Answer 1

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.