Finding the Slope of Horizontal and Vertical Lines | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover the slopes of horizontal and vertical lines. We will start with horizontal and then move on to vertical. We will go through two examples for each. One where we find the slope from a graph and one where we find the slope from two points. Let's jump into number one where we have a horizontal line graphed on the coordinate plane. Now remember slope measures the steepness of a line. So how much a line moves up or down as it moves from left to right. Here we can see that this line isn't moving upward or downward at all. So what is the slope going to be? Well, let's find the slope of this line using these two points on the line. So we need to figure out the rise and run. Remember, the slope equals the rise over the run. The vertical change over the horizontal change. Let's start with the rise. And we're going from the left point to the right. Well, there isn't any vertical change. The line just goes straight across. So, the rise is zero. Now for the run, the horizontal change, we go over one unit, 2 units, 3 units, four units to get to the other point. So our run is four. So slope equals rise over run. So our slope here for this line equals the rise of zero over the run of four. So 0 over 4. That's our slope. Now any fraction with a numerator of 0. So a top number of 0 equals just 0. So we can also write this as just zero. We would say that this line has a slope of zero. And that goes for any horizontal line. Any horizontal line has a slope of zero. the y values stay the same as we move across the line and the x values increase. For this line in particular, the y value of any point is going to be two. So again, any horizontal line has a slope of zero. Let's move on to number two where we are going to find the slope of the line from two points on the line. So we just have the coordinates, no graph here. Remember, we use the formula slope equ= y2 - y1 over x2 - x1. y2 - y1 gives us the rise and x2 - x1 gives us the run. So, slope equals y 2 - y1 over x2 - x1. Now, let's label and plug in. So for -13 this is going to be our first point. So x1 and y1 -1 is x1 and 3 is y1. Then for 53 that's going to be our second point. So 5 is x2 and 3 is y2. Now we plug in. So y 2 is 3 minus y1 is 3 over. And now we need x2 5 - x1 -1. And I'm putting -1 in parentheses there just so it's clear. We are working with a negative. And it doesn't get lost next to that subtraction sign. And now we subtract. 3 - 3 is zero. And then we have 5 - -1. Now, whenever we have a subtraction problem involving integers and we have positives and negatives, it can be helpful to add the opposite and this is one of those problems. So, let's add the opposite. The opposite of - 1 is pos 1. So, we have 5 + 1 that gives us six. So, our slope here is 0 over 6. We have that numerator of zero. So, we can just write this as zero. So we have a slope of zero here. That tells us we have a horizontal line. And if we look at the coordinates here, we can see that we have the same y-coordinate 3 and three. So there's no vertical change between these two points. So again, this is a horizontal line. So there you have it. There's the slope of any horizontal line. Let's move on to vertical lines. Now we're going to take a look at the slope of a vertical line. Let's jump into number one where we have a vertical line graphed on the coordinate plane. Here we can see with this line there's vertical change but no horizontal change. There's no movement left or right at all. So what's the slope going to be? Well, let's find the slope using these two points on the line. So, we need to figure out the rise and the run. Let's start with the rise. And we're going to go from that bottom point to the top point. We go up one unit, two units, three units in order to get to the other point. So, our rise here is three. Now, for the run, the horizontal change, well, there isn't any horizontal change. The line just goes straight up and down. So, the run is zero. So our slope equals the rise over the run. We have a rise of three and a run of zero. So we end up with 3 over 0. Now whenever we have a fraction with a denominator of zero, so a bottom number of zero, we have something that is undefined because we are dividing by zero. Dividing by zero is undefined because we can't divide by zero. So whenever we have a vertical line, we always end up with a run of zero. Therefore, a denominator of zero. Since the denominator is zero, that gives us an undefined slope. So our slope here is undefined. So we would say that this line has an undefined slope and that goes for any vertical line. The y values for a vertical line change but the x values do not. So we always get that run of zero. Let's move on to number two where we are going to find the slope of the line from the two points on the line. So we just have the coordinates no graph here. So slope equ= y 2 - y1 over x2 - x1. Now we need to label and plug in. Our first point is going to be 42. 4 is x1 and 2 is y1. 47 is our second point. So four is x2 and 7 is y2. Now let's plug in here. So y2 is 7 - y1 is 2. Then we need x2 and x1. x2 is 4 - x1 is 4. So 4 - 4 there. Now we subtract 7 - 2 is 5 and then 4 - 4 is 0. So we end up with 5 over 0 for our slope. So we have that denominator of zero. That tells us we have a vertical line here and the slope is undefined. And if we look at the coordinates, we can see that we have the same xcoordinate of four here. So there's no horizontal change between these two points. This is a vertical line. So there you have it. There are the slopes of horizontal and vertical lines. Horizontal lines slope of zero. Vertical lines undefined slope. I hope that helped. Thanks so much for watching. Until next time, peace.