in this video we're going to talk about how to find the slope and Y intercept from a linear equation now it's important to be familiar with the slope intercept form of a linear equation and here it is M represents the slope m is a number in front of x b represents the y intercept so if we were to write the slope intercept equation right below this one we can clearly see that M which is the number front of X that's two and B is the constant uh that's three so in this problem the slope which represents m is 2 and the Y intercept which is equal to B that's three so that's a quick and simple way of how you could find the slope and a y intercept from the equation however not all examples are simple as this so we're going to cover a lot of examples in this video go ahead and try these two examples let's say Y is equal to 34 x - 5 and also Y is = 8 - 4x so feel free to pause the video and try those examples if you want to so for number two we can see that the slope is just a number in front of X so the slope is going to be 3 over 4 and the Y intercept is the number other than this it's the constant without the X so it's -5 now for the next example it's not written in slope intercept form but we can change that if we were to switch to 8 with the -4x and write it this way we get -4x + 8 keep in mind there's a plus in front of the eight you just don't see it immediately so writing it this way we can see that the slope is -4 and the Y intercept is 8 if it's not given to you in slope intercept form you need to adjust the equation and put it in slope intercept form once in slope intercept form you could find the slope and the Y intercept go ahead and try these two examples let's say we have y is equal to 5 - x and also Y is equal to -7x so for the fourth example I'm going to reverse or switch to five in the negative X so this ISX + 5 now you might be wondering what is the slope here we don't really have a number if you don't see a number there this assume it's always a one so this is --1x + 5 that's the same ASX + 5 therefore the slope for this line is -1 and the Y intercept is five so that's it for number four now what about number five all we have is just a -7x it doesn't appear to have any B value in a situation like this you can rewrite this equation as follows so Y is equal to -7x + 0 -7x + 0 is the same as -7x and writing it this way you can clearly see that the slope is -7 but the Y intercept is is zero so that's all you need to do for that particular example now what about these two let's say if we have y is equal to 3 and X is equal to 4 what is the slope and Y intercept for these two lines I want you to think about that for a moment now for y equal 3 we can rewrite this um like this we can say it's Y is equal to 0x + 3 so this is in slope intercept form 0x + 3 is equal to 3 these two have the same value so we can clearly see that m is zero and B is three so for this problem the slope is zero and the Y intercept is three now what about for xal 4 because you can't really put that in slope intercept form so what do you do to get the answer there for xal 4 you need to graph it why equal three this is a horizontal line at three horizontal lines they have a slope of zero because they don't go up they don't go down they're just flat and you could see the horizontal line it touches the Y AIS this is the x- axis this is the y- axis it touches the y- AIS at three so that's why the Y intercept is three because that's where it touches the y- axis now for a vertical line x = 4 the situation is different so this is how we can graph xals 4 it looks like this for vertical lines there is no slope if you try to calculate the slope of a vertical line it's going to be undefined if you're wondering how you can calculate the slope of a horizontal or vertical line you could use this formula m is equal to Y2 - y1 / X2 - X1 so for the horizontal line if you pick any two points let's say this is y1 Y2 in both cases y1 and Y2 they'll have a value of three regardless of what x 1 and X2 is and so it's always going to be zero all the Y values on a horizontal line will have the same y value of three because Y is three it's always three anywhere on this horizontal line so this is always going to be 3 - 3 for this line giving you a slope of zero well for a vertical line X is always the same so these two points may have different V y values this may be y1 Y 2 but the x value is always four and so if you were to calculate the slope using this formula it will be Y2 - y1 but on the bottom X2 and X1 they're going to be four and so you're going to get a zero on the bottom and whenever you have a zero in the denominator of a fraction it's going to be undefined so for a vertical line the slope is always undefined now what about the Y intercept now this vertical line will it ever touch the y- axis the answer is no because it's parallel to the y- axis so it will never touch the y- axis therefore for the Y intercept there's none there is no y intercept so whenever you see an equation like this x equals some number the slope is going to be undefined and the Y intercept is just going to be nothing there's no Y intercept by the way for those of you who want access to more video related content feel free to check out the links in the description if you click on this more button you're going to see other videos relating to the video that you're currently watching and these links are separated by chapter and of course you could check out my website video.net where you'll get access to my video playlists final exam videos and also test prep videos so feel free to take a look at that when you get a chance so let's say if we have y = -6 and x = -2 so whenever you have y is equal to some number whether it's a positive or negative number the Y intercept is going to be whatever y equals and the slope is always going to be zero for this kind of line when you whenever you see x equals a number whether it's positive or negative the slope is going to be nothing and I mean the Y intercept is nothing but the slope is going to be undefined it's always going to be that way based on the explanation U that I gave you you for the last two examples now what would you do if you get a linear equation in this form so right now this linear equation is in standard form and in order to determine the slope and the Y intercept we need to put it in slope intercept form yal MX plus b so the way to convert it from standard form to slope intercept form is you need to solve for y in other words you need to get y by itself on one side of the equation so first we need to get rid of this two in front of Y and this term we we need to move it to the other side so what I want to do is get rid of the two first I'm going to divide everything by two so -4 / 2 is -2 2 / 2 is 1 so 1 Y is the same as just WR in y and 6 / 2 is three so we have this now I'm going to take this term move it to the other side on the left side it's -2X when I move it to the other side it will be positive 2x the other way to do this is to add 2x to both sides if you add 2x to both sides this will cancel here and we'll get Y is = 2x + 3 as you can see if you simply move it it changes from -2X on the left to positive 2x on the right and we can see that the slope is 2 and the Y intercept is three so that's it for this example let's try a somewhat similar problem let's say we have 3x - 5 Y is equal 8 go ahead and find a slope and a y intercept for this line so first I want to get rid of the number in front of Y so I'm going to divide both sides by5 so I'm going to have -3 over 5x these two will cancel so I'm just going to get + y5 /5 is POS 1 and then this equals -8 over 5 now I'm going to take this term move it to the other side so I'm going to get Y is equal to it's negative on the left but it's going to be positive on the right so POS 3 over 5x and then minus 8 over 5 so this is my M value m is a number in front of x m is 3 over 5 and this is my B value B is going to be -8 over5 so now I have the slope and the Y intercept now let's work on one more example let's say I have -2 7x + 3 7 Y is equal to 4 s so what should we do to convert this standard equation into its slope intercept form what would you do now just like before I want to get rid of the 3 over 7 in front of the Y but if I divide everything by 2 7 that can make the math a bit complicated so because I have fractions and I want to get rid of the fractions I'm going to multiply everything by seven doing this all the sevens will cancel with this seven so I'm going to get -2x + 3 Y is = to 4 next I'm going to get rid of the 3 in front of the Y by dividing everything by 3 so I'm going to get -2 over 3x 3 over 3 is 1 so this is just going to be + y is equal to 43 then I'm going to take this term move it to the other side and I'll get Y is equal to positive 2 over 3x + 43 and so I could see that the slope is POS 2 over3 and the Y intercept is 4 over 3 so that's how you could find the slope and the Y intercept from a linear equation all you have to do is convert it to slope intercept form and identify your m and B values so that's it for this video uh thanks for watching for those of you who want more videos on algebra linear equations feel free to check out the links in the description section below thanks for watching