The Key to Graphing Equations

What do you think of when you hear the term, slope? Do you think of a skier, skiing down a large mountain?

Or, maybe you think of the sliding board at the playground.

Whatever you are thinking, it's probably something that's on an incline! When we study slope in Algebra we are going to study the incline and other characteristics of a line on a graph.

Slope is a very important concept to understand in Algebra. Therefore, I've created three different lessons to help you gain a full understanding.

We will start here with defining and calculating slope by analyzing a graph. Then we will move on to graphing slope and finally to using slope intercept form to create your graph.

Start here from the beginning, or move onto the concept of slope that you need help with!

Slope is used very often in Mathematics. It can be used to actually find how steep a particular line is, or it can be used to show how much something has changed over time. We calculate slope by using the following definition.

In Algebra, slope is defined as the rise over the run. This is written as a fraction like this:

- Find two points on the line.
- Count the rise (How many units do you count
**up or down**to get from one point to the next?) Record this number as your numerator. - Count the run (How many units do you count
**left or right**to get to the point?) Record this number as your denominator. - Simplify your fraction if possible.

- If you count
**up or right**your number is positive. - If you count
**down or left**your number is negative.

There are two examples below. You can watch how I calculate slope in the video lesson, or you can skip the video and check out examples 1 and 2 below.

Example 1: Calculating Slope

Let's take a look at another example where the slope is a fraction.

Slope is a fraction: rise/run. Calculate your rise and then your run!

If your rise is **downhill** it is negative. If your run is to the **left** it is also negative!

You can choose **any** two points on the line to calculate your slope! The slope is constant throughout the
whole line.

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