How to write an equation of a line in slope intercept form with two points?

The slope-intercept form of the equation of a line is

y = mx + b

1) Use the two points to find the slope.
Subtract the y-coordinates.
Subtract the x-coordinates int eh same order.
Divide the difference in y by the difference in x.
That is the slope, m.

2) Now you need to find b.
Rewrite y = mx + b with your value of m in the equation.
Now use one of the two points and replace x and y with the x- and y-coordinates and solve for b.

3) Finally, rewrite y = mx + b with the values of m and b you found.