How to find an equation in slope intercept form given two points?

Example :

(1,2)(3,4)

first we find the slope by using the slope formula
slope = (y2 - y1) / (x2 - x1)
now we label our points..
(1,2)...x1 = 1 and y1 = 2
(3,4)...x2 = 3 and y2 = 4
now we sub and find the slope
slope = (4 - 2) / (3 - 1) = 2/2 = 1so we have a slope of 1

now we use y = mx + b
slope(m) = 1
use either of ur points...(1,2)...x = 1 and y = 2
now we sub into the formula and find b, the y int
2 = 1(1) + b
2 = 1 + b
2 - 1 = b
-1 = b this is ur y int

and in y = mx + b form, the slope will be in the m position and the y intercept will be in the b position

y = mx + b
slope(m) = 1
y int (b) = -1

so ur equation in slope intercept form is : y = 1x + (-1) which can be written as : y = x - 1