Question

Write an equation in point-slope form of the line through these given points.I need separate answers for each problem, thx

Answer 1

I like point point form because it doesn't fail in the no slope case.  The line through (a,b) and (c,d) is

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

Point slope form is almost the same,

$y - b = \dfrac{d-b}{c-a} (x-a)$

1. (a,b)=(4,0),(c,d)=(-2,1)

y - 0 = (1 - 0)/(-2 - 4) (x - 4)

Answer: y = (-1/6)(x-4)

2.

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

Answer: y + 2 = (5/8) (x+3)

3.

y - 1 = (4 - 1)/(3 - -5) (x - -5)

Answer: y - 1 = (3/8) (x+5)