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Finding the Slope of a Line from 2 Points - Concept

Teacher/Instructor Alissa Fong
Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

If given the equation of a line, or two points on the line we can try to find the slope of a line from two points. This is often the most efficient way to calculate slope, and can be done with a simple formula to find rise over run. Finding the slope of a line from two points requires us to know the definition of slope. and how to plot points.

You guys know that it's not so hard to find the slope off of a graph. But sometimes it can be kind of tedious if a graph isn't provided for you.
I don't know about you, but, I don't like graphing. I think it takes a long time. So I like shortcuts that only use Algebra. And the cool thing is, there's this handy formula that can tell you the slope of a line even if you never graphed it. And in order to use this formula you need to know two points that the line passes through. You can use any two points you want to. And the way you would find the slope is by subtracting the y coordinates and then subtracting the x coordinates and writing that as a ratio.
One thing that's super important though, please please please make sure that if you start your y value from one point, you start with the x value from that point also. That's why we use these little subscript numbers to help us remember like the y value from my second point, take away y value from my first point. Go back and use that same original point. x value from that guy take away the other x value. It's important that you start from the same point when you're doing your subtraction.
This is a formula that you're going to want to have memorized. If you want to you can write it on your hand until it sticks in your head or whatever. However, you can get this formula into your brain, this is something you're going to want to use for the rest of your algebra career.

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