Question

What is the equation in point-slope form of the line passing through (4, 0) and (2, 6)?

Answer 1

First we find the slope using the slope formula :
slope(m) = (y2 - y1) / (x2 - x1)
(4,0) x1 = 4 and y1 = 0
(2,6) x2 = 2 and y2 = 6
now we sub
slope(m) = (6 - 0) / (2 - 4)
slope(m) = -6/2 which reduces to -3
so now we know that the slope is -3.
Now we can use our point slope form :
y - y1 = m(x - x1)
slope(m) = -3
use either of your set of points...(4,0) x1 = 4 and y1 = 0
y - 0 = -3(x - 4) === >point slope form

or if you used the other points (2,-4)
y - (-4) = -3(x - 2)
y + 4 = -3(x + 2) ===> point slope form