in this video I'm going to provide a list of formulas associated with linear equations so the first one we're going to talk about is called the slope intercept form of a linear equation in this equation M represents the slope of the line and B is the Y intercept let's briefly talk about the intercepts so let's say we have this graph this is the x intercept I mean not the x intercept but the x- axis and this is the y- axis and let's say we have a line that looks like this now the point that touches the X AIS that's going to be the x intercept so that's -3 I'm just using a random number let's say this is four four is the Y intercept the Y intercept is the point or the Y value at which the graph touches the y axis the x intercept is the x value where the line touches the x- axis so in this case the x intercept as an ordered pair is -3 comma 0 and the Y intercept is 04 so at the x intercept Y is z and at the Y intercept X is z so that's how you could find it graphically by the way for those of you who want more examples I'm going to be posting a few links in the description section below so you could see how to use some of these formulas now for this equation if you want to calculate the x intercept for the x intercept I'm going to call it x i you know just because it has wrri in the x intercept is going to be b/ M if you set y = z and solve for x you're going to get b m so that's how you can find the x intercept from this equation now if you need to calculate the slope if you have two points you could use this formula the slope is Y2 - y1 / X2 - X1 the change in y values represents the rise between two points and the change in X values represents the run so let's say if you have a point here and a point here and you want to determine the slope of this line let's say this point is 2 comma 3 and this point is 57 well to go from 2 to 5 along the x- axis you need to travel three units 5 - 2 is 3 and they go from 3 to 7 across the y AIS you need to travel up four units so the rise is four the run is three which means the slope of the red line is 4 over 3 so that's how you could use the rise overrun formula to determine the slope between two points now the next equation is called the point slope formula of a li a linear equation so this is the point slope form in order to write a linear equation in this form you need two things you need the slope M and you also need a point which is X1 and y1 so notice the difference between X and X1 X is just a variable X1 is the x coordinate of the point so that's all you need to know with this formula now the next form of a linear equation is called the standard form and it's ax + b y is equal to C now if you have an equation in this form if you want to determine the slope you could use this formula the slope of the line is going to be A over B the Y intercept if you set x equal to Z and solve for y you'll get that Y is C over B and to get the x intercept by the way if you see lowercase b is the same as the Y intercept you can write this as y sub I is equal C over B now to get the x intercept if you set y equal to Z and solve for x you'll get that X is equal to C / a so if you have a linear equation in standard form you can get the slope the Y intercept and the x intercept using those formulas for those of you who want to derive this equation what you can do is you can solve for y convert this equation in slope intercept form and the term in front of X will be the slope so remember in slope intercept form it's y = mx + b m the number in front of X represents the slope so if we were to solve for y in this equation we would have to move ax to the other side so we would get b y is equal to ax + C and then what we would do is divide div everything by B so these will cancel and now we'll have y isal to A over B * x + C over B so notice that this equation is now in slope intercept form so the number in front of X which is M notice that it's negative A over B so we can see that they're equal here B is the Y intercept which is C over B and that's what we have here and to get this one all you need to do is set y equal to Z and solve for x and it's going to be C / a but those are the three formulas that will help you to calculate the slope the Y intercept and the x intercept if you have a linear equation in standard form by the way for those of you who want a printed formula sheet with these equations feel free to check out the links in the description section below now the next one is an uncommon form of a linear equation I'm not sure if you heard of this but it's called the intercept form not the slope intercept form but the intercept form of a linear equation and it looks like this it's x/ a + y b is equal to 1 notice that I didn't use capital A and capital B the reason is because lowercase b represents the Y intercept so if you have a linear equation in this form this has to be one it can't be anything else a is equal to the x intercept B is equal to the Y intercept and the slope SL is simply b/ a keep in mind the slope is the change in y / the change in X so it's fitting that it's going to be negative B over a so that's the intercept form of a linear equation now when you have two lines let's say these lines are parallel let's call this line one line two so line one is parallel to line two what you need to know is that parallel lines they have the same slope so the slope of line one is equal to the slope of line two now let's say this is line one and line two meets line one at a 90° angle line one is perpendicular to line two so when dealing with perpendicular lines you need to know that the slopes are negative reciprocals of each other so M1 is going to be equal to 1/ M2 so for instance let's say L1 one has a slope of POS 3 over 5 L2 the slope is going to be negative but it's going to be the reciprocal of that fraction so it's going to be- 5 over3 so that would be an example of calculating the slope of a line that's perpendicular to another line now when dealing with horizontal lines a horizontal line always have a slope of zero and the equation of a horizontal line is going to be y equal K where K is some number when dealing with vertical lines the slope is undefined and the equation is going to be x equal to H where H is some number so I'll give an example let's say we have this graph and let's say we have a vertical line here what is the equation of that vertical line notice that it touches the point x = 3 so it's always at xal 3 over here x is still three over here x is three so so it's always x = 3 so that's why I have the equation x = h a vertical line will always be xal some number now for a horizontal line it's going to be Y is equal to some number so notice that this line touches it has a y intercept of two so this horizontal line is just going to be yal 2 so for horizontal lines it's y equal K where K is some number you just have to find where it touches the Y AIS and for vertical lines is xal H H is basically the x intercept which is in this case three