# How to Find:

## Formula:

The formula for slope is sometimes referred to as "rise over run", because the fraction consists of the "rise" (the change in y, going up or down) divided by the "run" (the change in x, going from left to the right). 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. The point is that slope tells you how much y is changing for every so much that x is changing.

## Where to start:

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"); that is, 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:

## Examples:

Let's look at these two points on the graph:
In stair-stepping up from the first point to the second point, our "path" can be viewed as forming a right triangle:

To get to the "next" point, we can go up another two (to y = –2), and over to the right another three (to x = 3):

With these three points, we can graph the line y = ( 2/3 )x – 4.

## Do it Yourself:

Find the following slopes:
Duck Song! (instrumental, yo!)