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Slope of a Line - Part 2

Another way of looking at slope of a line is looking at it as an equation. We talked about what it meant for rise over run before. So what we will talk about how is that slope m equals the change in y's over the change in x's. The way that we can conclude this type of equation is we have the second y which is denoted with a y sub 2 minus the first y which is denoted as y sub 1, divided by x sub 2 minus x sub 1. The subs mean that, say, if it were a 2, that means y sub 2, that is the y value that comes from the second point. Whereas, if it is a 1, it’s the y or x value that come from the first point. Say, for example, we wanted this point right here to be point 1. That means that this point here would be point 2. My point 1 is negative 1, 4 (minus1, 4). My point 2 is negative 4, 2 (minus4, 2). Now all we have to do is plug in our x's and y's. Remember that here is your x values, and the second number is your y values. To find our slope, we look at what y 2 is (the y value on the second point) which is this 2. Then minus our y1, which is our y value on our first point, which is this 4. We have 2 minus 4 for our change in y's . Now we must locate the x sub 2, which is the second point in our x values. So, it this negative 4. Then our x sub 1, which is the x value in the first point, we’ve got negative 1. Remember, since this is a negative, be very careful. We must still put the negative in there and then our x sub 1 which is negative 1. This is sometimes confusing because people suspect that they already have the negative there, but remember you are substituting in. So, you have to substitute the negative 1 with its sign. From here, all we have to do is simplify. The first part, 2 minus 4 is negative 2. For the second part (what's underneath) we have negative 4 and then those become pluses. So negative 4 plus 1 gives us negative 3. We have negative 2 divided by negative 3. A negative divided by a negative is actually a positive. The answer is positive two-thirds (2/3). Then, we start asking, "Does it matter which point we make first or second?" No, it doesn't. You should always get the same answer. So let's try it. Let's erase all of this. This time, this is going to become point one, and this will be point two. So I've got point one being negative 4, 2 (minus4, 2) and point two being negative 1, 4 (minus1, 4). Our slope is the change in y's , our second y is this 4 here. Then minus our first y which is our 2 divided by our second x which is negative 1 minus our first x which is negative 4. Remember that you are subtracting a negative 4, which, in turn, becomes positive 4. So, 4 minus 2 gives us 2. Negative 1 plus the 4 gives us positive 3. Notice it is the same idea. Just remember, if you start off with saying this is going to be my first point, you must keep it as your first point. A lot of times we tend to get those mixed up in the x’s and y’s.

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