Math 1A/1B. Pre-Calculus: The Slope of a Line

let's learn about the slope of a line for example let's find the slope of the line passing through these two points here the slope of a line measures its steepness and can be computed by the following formula that the slope M is the difference in the Y coordinates of the two points which we call the rise divided by the difference in the x coordinates which we call the run so let's let x1 y1 be our first point over here this negative 4 negative 3 and X 2 y to be the second point namely 8 negative 9 so by this formula we have M the slope is equal to y 2 which is negative 9 here minus y 1 so minus a minus 3 be careful / x 2 which is 8 minus x1 which is negative 4 which is equal to negative 9 plus 3 is negative 6 divided by 8 minus a minus 4 is 12 which means that we just found that this rise of a run down here is equal to negative 6 over 12 so we can think of negative 6 as the rise and 12 as the run and let's look at what this means the run is positive 12 which means from that point negative 4 negative 3 we're going to go to the right 12 and then the rise is negative 6 so we go down six to get to that other point let's see what happens if we compute em the other way in other words let's let this point 8 negative 9 be x1 y1 instead so if we let x1 y1 equal 8 negative 9 + x2 y2 be equal to the other point negative 4 negative 3 then by this formula we get M is equal to y 2 which is negative 3 minus y 1 so minus a minus 9 divided by X 2 which is negative 4 minus x1 which is 8 which is equal to 6 divided by negative 12 so now we can think of our run as being negative 12 and our rise as being 6 that is from our first point 8 negative 9 our run is negative 12 s we go to the left 12 and our rise is positive 6 so we go up six units to get to the other point so it doesn't matter which way we label our points in either case we get that our slope is equal to negative 6 over 12 which is negative one-half let's look at another example let's find the slope of this line that's graphed here alright so this is the point negative 1 negative 2 and this is the point 2 3 again we're going to apply our slope formula here that the slope is y2 minus y1 divided by x2 minus x1 so let's let this point be x1 y1 and this point be x2 y2 by our formula here m is equal to y2 which is three minus y1 which is negative two divided by x2 which is two minus x1 which is negative one or 5/3 so we can think of our run as being positive 3 and our rise as being 5 which means starting at our first point we go to the right three units and then up five units to get to our second point now we could have done it the other way right we could have let this point here BR x1 y1 and this point here BR x2 y2 so by our formula then the slope would be equal to y 2 which is negative 2 minus y1 which is 3 divided by X 2 which is negative 1 minus x1 which is 2 or negative 5 divided by negative 3 so the run is negative 3 rise is negative 5 that is from our first point we go to the left 3 units and then down 5 units to get to our second point but in either case we get that the slope is equal to 5 thirds and this is how you compute the slope of a line thank you and we'll see you next time you