Calculating Slope
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!
What is Slope in Algebra?
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:
Rules for Calculating the Slope of a Line
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.
IMPORTANT NOTE:
If you count up or right your number is positive.
If you count down or left your number is negative.
Let's look at an example:
Example 1
Example 2
Your turn to practice calculating slope!
Remember, choose two points and calculate your rise over run! Don't forget to look for negative slopes:
If you count down or left!
Your Turn to Calculate Slope!
Answer Key for Calculating Slope
1. The slope of the line is 1/4.
2. The slope of the line is 1/3.
3. The slope of the line is -2/3
4. The slope of the line is -2.
5. The slope of the line is -1.
Great Job! Just remember that 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.
Now you are ready to move onto Graphing Slope!
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