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Finding the Slope of a Line from 2 Points - Problem 3 4,834 views

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

When given two points on a line, you can use the slope formula, m=(y2-y1)/(x2-x1), to find the slope of the line. Remember that the coordinates of the first point represent x1 and y1, and that the coordinates of the second points are x2, y2. It does not matter which point you label as the first point and which you label as the second. Don't forget to include the correct sign of each value. Simplify to get the value of the slope. If the result is 0, that means that the line is horizontal. Check the your answer by graphing the points to see if the points are, indeed, part of a horizontal line.

In this problem, I’m asked to find the slope of the line that goes through two points. So I could graph it, but I think you guys maybe are like me you don’t always like graphing especially if you don’t have graph paper handy, that’s why we have this great formula; slope is equal to y2 take away y1 on top of x2 take away x1. So if I go through and do that calculation, we’ll see how it goes. Y2 take away y1 on top x2 take away x1 and then let’s simplify that.

4 take away 4 is 0, 2 minus -3, the minus-minus becomes plus, so I have zero over, oh that’s weird huh? 0 over 5, you guys probably know from your study of fractions that zero divided by anything is just plain old zero, so I think that’s my answer, but when I come to a problem like this, one thing I might try to do is do a graph, even though I’m not a huge graphing fan, since I got a weird answer, I’m going to try to check my work by graphing.

So let’s make a really rough sketch (-3,4) something like that (2,4) there it is. I’m looking at the line that goes through this, that's like the worst line hang on pause talk amongst yourselves let me fix this really quickly. (-3,4) I’m just trying to make this a little easier to see, okay that’s better. The reason why I got this funny answer zero is because I got it flat line, or officially a horizontal line. This line doesn’t change vertically at all that’s why I had a zero on top of my fraction. The vertical change is zero.

So any time you have a horizontal line where the equation looks like y equals something or rather in our case it’s y equals 4, your slope number is going to be zero. That’s something that’s really critical to keep in mind, and it’s really easy to get confused in your brain. This horizontal line is like this one or that one or whatever. Any time you get a horizontal line or something y equals some constant, the slope of that line is going to be zero. So the way I checked that is using the formula here, y2 taker away y1 over x2 take away x1 and you can see then I got that the same ratio zero.