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Finding the Slope of a Line from 2 Points - Problem 4
Use the slope formula, m=(y2-y1)/(x2-x1), to find the slope of the line given two points on the line. The coordinates of the first point represent x1 and y1, and 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 undefined, meaning the denominator of the slope is 0, that means that the line is vertical. Check the your answer by graphing the points to see if the points are, indeed, part of a vertical line.
This is a problem where I’m asked to find the slope and I’m given two points. So rather than graphing, I’m going to use my favourite formula, it’s not really my favourite formula, but I like it. For the slope, let’s go ahead and plug in the numbers 3 take away -1 on top, 2 take away 2 on the bottom and then simplify. On top 3 take away -1 is +4 and then on bottom there I get zero.
Look out you guys that should be like bells and whistles going off in your brain. One of the Math laws is, thou shall not divide by zero, so what this tells me is that this slope is like not possible, or what we call it in Math is undefined, or you could also sometimes call it, no slope.
If you tried to do 4 divided 0 on your calculator, you would get error, it would send you like either little 'e', or it would say the word 'error'. It tells you that this is an undefined value in Mathematics. Let’s look at the graph just so you guys believe me, and I can show you what the graph looks like in the situation where we have an undefined slope.
So let me come over here, so I’m just going to draw a really rough sketch (2,-1) and (2,3) there are those two points. I’m looking at the vertical line that goes through them. Well my line almost goes through them you get the idea, let’s make both points a little bigger, all right now it goes through them. A vertical line has the equation x equals some constant, in our case it’s x equals 2, and the slope of a vertical line is always going to be undefined, or you could also call it no slope, depending on your teacher or your textbook, either one of those is a fine way to describe it.
So if you do a problem using the slope formula and you get something funny, and you know thou shall not divide by zero, it’s okay you’re just getting this unique situation in which you have a line with an undefined slope.