Today we’re going to find the slope or gradient from two different points on the axis. So here I have 2, 3 and 6,4 and my first point, 2,3...I have the x value of 2 and y the value 3. You have to be able to determine which one is the x and y and x is always the first number, y is always the second number. So I have the ordered pair, 6,4, my x value is 6 and my value is 4. So to find the slope of this line using these two points there is a formula that we have to use and slope, from now on, I’m going to use the letter m to represent that, but slope is going to be the change in my ys or my y value over top or divided by the change in my in my xs. And if you take a look at the graph, a dot...actually I’m going to draw because that’s not looking real pretty...my change in my ys and my change in my xs are simply how far apart are my points along the x axis and how far apart are the points along the y axis. So this would be what we consider our change in xs and up here is our change in ys, but we’re going, for now, use subtraction. We’re going to use a standard little formula where we subtract our ys on the top and we subtract our xs on the bottom. You may also see that written like this: y2 minus y1 over x2 minus x1. That simply means that you are subtracting the 2 ys and they use that little subnumber two and one to signify that you’re using two different y values. If you look at your ordered pairs, y equals 3 and y equals 4, you have two different y values. The only thing you really need to do here that’s tricky, and it’s really not that big a deal, is to choose which point you’re going to start with. So I’m going to choose 6,4 because those are my higher numbers. And since I’m going to subtract, if I start with my higher numbers, I can avoid negatives. So I’m going to put my y value of 4 into the equation and I’m going to subtract the other y value of 3 from the other ordered pair. Since I started with 6, 4 on the top, I have to start with that same ordered pair on the bottom. So I’m going to take my x value of 6 from that ordered pair and subtract the other x value from the other ordered pair. So now I have 4 minus 3 which is 1 over 6 minus 2 which is 4. So my slope, or how far this line slants, is called 1/4th. You can also...you could have it a slightly different way by choosing 2,3 as your first...as the first number and if you had done, you should get the same answer as long as you do the math correctly. So if you choose 2,3 as the first ordered pair, then the y value there is 3, so you’re going to start with 3, subtract the other y value of 4; since you started with 2,3 on the top you’re going to start with 2,3 on the bottom, which means you do 2, which is x minus the other x, which is 6...your answer is...3 minus 4 is negative 1, 2 minus 6 is negative 4...negative divided by a negative is a positive. So your slope is 1/4th no matter how you do it as long as use the right point...the same point for both the starting points.

Our next graph that we’re going to take a look at is shown on the screen here with two points...negative 4, negative 1...here’s my x value, here’s my y value and negative 2, negative 2, my x and my y in that particular ordered pairs is exactly the same. So if I use the formula, m equals my difference in ys over difference in xs, I’m just going to choose which one to start with. And in this case I’m going to start with negative 4, negative 1. So my y value there is a negative 1, I’m going to subtract the y value in the other ordered pair. Now notice I have a negative 2 and I’m subtracting it. You want to be real careful with your negatives here. You are always going to take the difference of the numbers so if there is a negative, you’re subtracting a negative. So, I take a look at my first ordered pair and the x value is negative 4 so I’m going to put that on the bottom. Negative 4 minus the x value in the other ordered pair is also negative 2. In Algebra, what I can do when I subtract the negative, is actually turn that into a positive. So subtracting a negative is the same as adding a positive. So I’m going to rewrite this quickly...negative 1 plus two over negative 4 plus 2 and my numerator, my top number, negative 1 plus 2 is a positive 1 and on the denominator I get a negative 2. So my slope is negative 1⁄2.

So here we have a final set of points that we have on the graph and this set includes 2,3 and 1,1. Again, that first digit in the ordered pair is my x value and the second one is the y value. Go ahead and pause the video and see if you can calculate the slope on your own here and when you’re done, resume play and see how you do.

So now I am going to calculate my slope, which is my difference is ys and I’m going to write the formula out this time just to remind you over the difference in xs. So my y value in the first ordered pair, and again, just choose which one you’re going to start with...I’m going to go with 3 minus the y value of the second ordered pair is 1. Since I started with 3 up here I’ve got to start with 2 as well on the denominator. 2 minus 1 is my other ordered pair so on top I have a 2 and on the bottom I have a 1. So my slope is 2 over 1.