How to Find Slope from Two Points | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover how to find the slope of a line from two points on the line. Now, remember, slope measures the steepness of a line. So, how much it moves up or down from left to right. And slope equals rise over run. So, the vertical change over the horizontal change. So here for these examples, we're going to use the coordinates of two points on a line to find the slope of the line. We use this formula right here. So slope equals y 2 - y1 over x2 - x1. y2 - y1 gives us our vertical change, the rise. And x2 - x1 gives us our horizontal change, so the run. Let's jump into number one. And the first thing that we need to do is pick our first point and our second point. So we have 310 and 79. I like working from left to right. So the left point to the right point since we are looking for the slope of the line as it moves from left to right. But really either way will work. So again, we're going to work from the left point to the right point. So 310 is going to be our first point. And then 79 is going to be our second point. So let's label these. For 310, 3 is our x coordinate. So this is going to be x1. And then 10 is our ycoordinate. So that's going to be y1. 4 7 9 7 is the x coordinate, so that's going to be x2. And then 9 is our ycoordinate. That's going to be y2. Now, all we need to do is plug these into our formula. And I'm going to rewrite the formula in order to help us get it down. So slope equals, and remember, we can use m to represent slope. So y 2 - y1 over x2 - x1. Now we plug in. So y 2 we have 9 minus y1 we have 10 over x2 we have 7 - x1 we have 3. And now we subtract 9 - 10 gives us -1 and then 7 - 3 gives us 4. and we end up with -1 over 4 - 1/4. And this is our slope. Let's move on to number two where we have -6 -4 and -2 6. Again, we're going to work from the left point to the right point. So, -6, -4 is going to be x1 and y1. And then -26 is going to be x2 and y2. So slope equ= y 2 - y1 over x2 - x1. And now we can plug in. So we have y2 which is 6 - y1 that's -4. And I'm putting -4 in parentheses here just so it's clear. We are working with a negative and it doesn't get lost next to the subtraction sign over x2 which is -2 - x1 which is six. Now we can subtract. And remember, whenever we have subtraction problems involving integers and we have positives and negatives, it can be helpful to add the opposite. And for both of these subtraction problems, this can be helpful. So for 6 - -4, let's add the opposite. The opposite of -4 is pos4. 6 + 4 gives us 10. And then for -2 - -6, let's add the opposite. -2 + 6 gives us a positive 4. So we end up with 10 over 4, 104s, which is correct. But when it comes to slope, we want to look to simplify. And this can be simplified. We have a greatest common factor of two that we can divide 10 and four by. So let's divide both of these by two in order to simplify. 10 / two gives us five and 4 / two gives us two. 5 over two is our final simplified slope. 5 halves. So there you have it. There's how to find slope from two points. I hope that helped. Thanks so much for watching. Until next time, peace.