Slope Between Two Points
The slope of a line is nothing but how slanted the line is. In order to find the slope of a straight line you need to know any two points on the line. You may be asking yourself "does it matter which two points I choose?" and the answer is no. If you choose any two points on the line, and I choose two other points we will sill get the same slope.
Your teacher might have told you that the slope is the rise/run. What in the world does that mean? Well the rise means how many units did you rise from your first point to get to your other point. In other words, rise is the change in the y-value of your two points.
Run means how many units did you "run" on the x-axis to get from your first point to your second point. In other words, run is the change is the x-Value of your two points. Let's look at an example together.
Example
Let's look at the example on the left. You have a line that passes through many points. To find the slope you have to choose two points. Let's choose (1,1) and( 2,3). (Points are highlighted on the graph)
To find the slope we need to know two things:
1. The change in the y-values of both points
2. The change in the x-value of both points
1. The y-value of the first point is 1 (remember we label points x,y) the y-value of the second point is 3.
To get from 1 to 3, how many units did we "rise"? If you said 2 you are right. (rise=2)
2. The x-value of the first point is 1, and the x-value of the second point is 2. To get from 1 to 2 how many units did we "run"? If you said 1 you are correct. (run=1)
3. The slope is= rise/run=2/1=2
Slope Formula
Another easy and convenient way of finding the slope between any two points is by using the slope formula (see picture on left). Y2 and Y1 refer to the y-value of your first and second points. X2 and X1 refer to the x-value of your first and second point.
Warning: You must be consistent with your points. If you name the Y-value of your first point Y1 you MUST name your x-value of your 1st point X1. It does not matter which point you choose for 1 or 2 as long as you stay CONSISTENT.
Test Your Slope Skills
You think you mastered this topic? Check your skills by taking this short online quiz. http://cs.selu.edu/~rbyrd/math/slope/slo_ty.html
