for this video I'd like to talk about the concept of horizontal and vertical lines and you can see I have each of them pictured here where this blue line is the vertical line and the yellow line is the horizontal line and essentially we need to understand the key features of each of these lines namely we need to understand the slope of each of these lines so remember that slope the way we define it is that it's the rise divided by the run so essentially from one point to the next on a line say from this point to this point essentially how much does the function or the line rise and then we'll divide that by how much it goes left or right which we call the run so essentially you can think of this as how much the equation goes up and down versus or divided by how much it goes left and right so let's start with this horizontal line here so the slope which we usually denote with the letter M you write that up here so the slope of this line we know we're looking at just the rise divided by the run but in this case the rise would be zero because notice that if we just pick two random points on our line that the rise is zero it just does not go up and down at all so we have zero divided by the run and the run in this case would be two because we chose these points two spaces apart but it honestly doesn't matter which two points you choose if I chose this one and this one you still have zero divided by some number and zero divided by anything is equal to zero so the slope of this line is zero so slope is zero for a horizontal line and now we can consider the vertical line this line here in blue so again we want to look at the slope which is the rise divided by the run so I'm going to pick two random points we'll just use this point here and this point here and essentially that our rise it looks like in this case is too but our run how much we go left and right is zero because these points are the exact same x-value so there is no change in the x value so we essentially have division by zero which we can't do so for this particular case for these vertical lines we'd say that the slope is undefined simply because you can't divide by zero you just cannot do this and this result we would find by choosing really any two points on this line we could have chosen this point and even this point down here whereas our rise would have been a much higher number it looks like 8 but our run would still be zero so you would have in any of these cases you would have some number divided by zero and since we can't divide by zero we can conclude that the slope of a vertical line is always undefined and with all of this in mind let's now go through some different example problems so let's start this first one we just want to graph these two different equations we've the equation y is equal to minus 4 which I'll graph in this blue color and we have the equation x is equal to 3 which I'll graph and the yellow color so let's start with the X is equal to 3 so basically we want to find an x value of 3 and essentially all points on this line have this same x value so essentially all of these points going up notice they all have X values of 3 and essentially every point on this vertical line here would have an x value of 3 and looking at this Y is equal to minus 4 which we'll graph in blue essentially we want to find a y-value of minus 4 which would be right here and all points on this line would have that same Y value so essentially this would be a horizontal line through the Y value of negative or because if you consider any point like let's say five comma minus four this point on the line does have a y-value of minus four and that's true of every single point on this line so in other words let's say if we had X is equal to minus two you want to find this x value on your coordinate plane that would be right here and essentially every point on this line would have that exact same x value so that's how you know you're looking at points above and below since all of these have the same x value and then we can essentially just draw our line in and we have this other vertical line so now let's try a different type of problem so we're given this line where it looks like X is equal to minus two here and we're asked what the slope of the line is so remember that slope M is defined as the rise divided by the run and in this case if we just pick two random points like let's say this point here and this point here then our rise it looks like we don't go up and down at all so our rise would be zero and a run would be two and as we saw above if we chose really any two points like let's say these points here you would still end up with zero divided by some number so the slope for this horizontal line is simply equal to zero and if we look at this problem here so now we have a vertical line through this point minus five comma minus two and to answer questions like this it might be easier if you start by plotting this on a coordinate plane so let me quickly draw a coordinate axes so we need to plot the point minus five comma minus two so we go over five to the left on the x-axis and then down two so that would be this point right here and then we need a vertical line through that point so let me just draw that and the key feature of this line is that they all have the same x value namely every point on this line has an x value of -5 so we can say that the equation of this line is simply X is equal to minus five and again this is just because every single point on this line has this exact same x value let's do one final example problem here and for this one we just need the equation of the line so what you can notice is that every point on this line has a different Y value but they all have the same x-value they all have this x value of minus 9 so we can say that the equation of this line is simply X is equal to minus mountain