Learn about the Slope of a Line In this lesson let’s learn how we find the slope of a line given what we know. So we will use let’s call the slope formula to determine the slope. What is the slope formula? Slope formula basically is rise over run. Rise is difference between the y points and run a difference between the x values. So let me give you a real example if we have any two points on a line here is A and B if the coordinates of A are x1 and y1 and coordinates of B are x2 and y2 right if this other two points on a given line then the slope of the line equals the difference in that y values over the difference in there x values. This is the key thing to remember, this is called the rise difference between the y points the high of the line and the difference between the x points are called the run. So let’s use this to calculate the slope here. Here y2 is the y coordinate of point b which is 5 so in this case it is 5 minus what’s the y coordinate of point A well at 3 over the x coordinates. X coordinates of line is point 2b are well it’s at 7 and the x coordinate of point 1, point a is 2. So the rise equals 5-3 which is 2 the run equals 7-2 which is 5 so the slope of this line is 2/5. Key thing to remember is the slope as positive the line will always go up, up to the right. So this is line is going up to the right you can see that the slope is positive this is a good way to check your answers. Let’s try one more we’ll do a few of this. In this case here’s point B here’s point A so what’s y2 – y1 over y2 – x1 that’s what we’re looking for right that’s the slope. So y2 is y coordinate of the second point which is 4 what’s the y coordinate of the first point well that sounds a 4. What about the x coordinates x coordinates for point 2which b is 6 and here it is 3. So it is 0/3 which is 0. If the slope is 0 then the line is a horizontal line that means that’s not going up, it’s going down it’s just going straight across. That means the slope is 0. Easy we will check our answers let’s try the 3rd one. Here we see this is point 1 this point 2. So let’s apply y2 - y 1 over y2 – y1 what do I get, y2 is second point what’s the y coordinate that’s -3- y 1 what’s the coordinate of point 1, y coordinate is 5 and x2 is x coordinate of B which is 4 and x coordinate of A is also 4 which means -8/ 0. We can’t divide 8 or any number by 0 that’s infinity or not defined. So this is not defined if a line has a slope that cannot be defined it is a vertical line that means the slope is infinity anything divided by zero. Let’s do one last problem. Here we see I’m just going to quickly do it what’s the y coordinate of line B or point B that’s y coordinate is 2.So y2 – y1 is 2 – y1 is 6 over x2 – x1 x coordinate of point B is 6 and y x coordinate of point a is 2 which is - 4/ 4 or -1. If the slope is negative the line is going down to the right. Similar to what we saw if the line is going to the top it’s going upwards as it goes left to right the slopes has to be positive. If the line is going down to the right then the slope has to be negative.