Using Slope and y-Intercept to Graph Lines

Given two points (x₁, y₁) and (x₂, y₂), the formula for the slope of the straight line going through these two points is:

...where the subscripts merely indicate that you have a "first" point (whose coordinates are subscripted with a "1") and a "second" point (whose coordinates are subscripted with a "2"). The subscripts indicate nothing more than the fact that you have two points to work with. Note that the point you pick as the "first" one is irrelevant; if you pick the other point to be "first", then you get the same value for the slope:

The formula for slope is sometimes referred to as "rise over run", because the fraction consists of the "rise" (the change in y) divided by the "run" (the change in x). If you've ever done roofing, built a staircase, graded landscaping, or installed gutters or outflow piping, you've probably encountered this "rise over run" concept.

Pictures can be helpful, so let's look at these two points.

We have (–3, –6) is on the line and so is the point (0, –4). Now that we have two points on the line, we can find the slope of that line from the slope formula:

Look at these 2 points on a graph

Stair-stepping up from the first point to the second point.