Step 3) Substitute either point into the equation. You can use either
(-3 , 6) or (15, -6)

Step 4

Step 4) Solve for b

Step 5

Step 5) Substitute b, -1, into the equation from step 2

Example 2: Equation from 2 points using Point Slope Form

As explained at the top, point slope form is the easier way to go. Instead of 5 steps, you can find the line's equation in 3 steps, 2 of which are very easy and require nothing more than substitution! In fact, the only calculation, that you're going to make is for the slope.
The main advantage, in this case, is that you do not have to solve for 'b' like you do with slope intercept from..

Find the equation of a line through the points (3 ,7) and (5,11)

Step 3) Substitute either point into the equation.
(-3 , 6) and (15, -6)

using (-3, 6) :
y − 6 = (x + 3)

using (15, -6) :
y + 6 = (x − 15 )

If you read this whole page and looked at both methods (lope intercept fro and point slope, you can see that it's substantially quicker to find the equation of line through 2 points by means of point slope.