Stony Brook MAT 123 Fall 2015
The Slope of a Line

Start   in this module we're going to learn how to find the slope of the line this is something that you all learned a long time ago but some of your little rust go over it again so first of all what is the slope of a line those are XY axes slope of line is measured by as they call it the rise over the run which is another way of saying every time I go out this much I go up that much so if I go out this
0:31much again I should go out that much again and of course the line does that so slope of a line is basically a way of measuring how fast it's going up for how slowly it's going up so every time I go to the right certain unit and go up certain amount number of units so in practicality how do we measure that well im gonna erase these so we can redraw it
1:02that's our line if I want to know how far I'm going out that's my change in my x coordinates so to find this distance I just take the difference between x1 x2 either way it doesn't really matter which when you subtract as long as you're consistent because you want to get the sin right know this that this distance will be y1 minus y2 and then I went to ratio so I
1:37want to know how much does y go from y1 to y2 when X goes from x 1 to x 2 for or as I said you could do it in here the work y2 minus y1 over x2 minus x1 it doesn't really matter as long as you're
2:00consistent so for example suppose I have a line that goes through two points 5 12 8,20 going slope but we abbreviate with the letter M but we indicate the letter m and is the difference in the y's over the difference in the X's and as I said it doesn't matter which order is as long a your consistent so the right 1 minus the
2:32left one the right one minus the left one and that's the third that means is every time you got three units to the right you go up eight units or if you go one unit to the right you go up eight/thrid units ok it's very straightforward now slope as a couple of things we need to make sure we are aware of when you go this
3:00and we do slope we're going to get a positive number positive so how do we know well the difference between this X this X positive number will be a bigger number minus the smaller number and that will correspond to a bigger y minus the smaller y if I'm going down on the other hand you get a negative slope
3:33because now yeah because now when i take x1 and subtract x2 i get a positive number but if i
4:05take the matching y1 i subtract Y2 which is bigger we are going to get a negative number let's use that means to see so suppose that's three and that's 10 and this is the point 3 comma 20 and this is the point 10 comma six then x1 minus x2 im sorry y1 minus y2 over x1 minus x2 will be 10-6 no it's not
4:4020-6 6-20 over 10-3 so y1 is 16 y 2 is 20 x 1 is 10 x2 is 3 so its negative 14 / 7 or
5:00negative 2 so that's how you get a negative slope what about a horizontal line like this well notice y1 and y2 is the same when I have y1 minus y2 one top that's y minus x to the bottom y1 minus y2 is
5:33just going to be 0 because y1 and y2 are the same thing x1 and x2 are going to be different so I'm gonna get 0ver numbers this is going to come out 0 so this is zero slope for example suppose that's three that's ten that's the point 3 comma 8 and that's point 10 comma 8 the slope will be 8-8 over 10 minus 3 which is 0 in this last kind of slope
6:08what about a vertical line well now i'm going to zero probably the other direction so i have a vertical line and here the X's are the same at the ys are different so let's say that's the point 3 comma 5 and that's the points 3,10 then y1 minus y2 over x1 minus x2 is 10 minus 5 over 3 minus
6:41three which is 5/0, 5/0 it's kinda weird right that's zero that's undefined so we say that this kind of line has no slope or we could say has an infinite slope
7:03and you understand that more when you do calculus so slope is family by change by taking the difference the coordinates now if you have an equation of the line you can find the slope from the equation of the line lines can be in the form of this way you'll see this most often in calculus work sometimes like this which
7:36you saw more often for calculus either way this is the slope so if you have a line y equals 2x plus 7 slope is too if you have this equation y minus 4 is 3
8:00times X plus 1 the slope is 3 and remember this can easily be put into this point that's all you need to know that slopes