# How to Find:

### Slope Intercept Rise over Run

## 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 (*x*1, *y*1) and(*x*2, *y*2), 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:

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!)