Question

What is the equation in point-slope form of the line passing through (-2, -5) and (2, 3)

Answer 1

point slope
the equaiton of a line passing through the point (x1,y1) and having a slope of m is
y-y1=m(x-x1)

and the slope between 2 points, (x1,y1) and (x2,y2) is (y1-y2)/(x1-x2)

so
find slope first

(-2,-5)
(2,3)
slope=(-5-3)/(-2-2)=-8/-4=-2/-1=2

m=2

pointn is (2,3) and (-2,-5)

the answer is
y-3=2(x-2) or
y+5=2(x+2)