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what is the equation of the horizontal line through the point negative 4 comma 6 so let's just visualize this once you get the hang of it you might not have to draw a graph but for explanatory purposes it might be used well so negative 4 comma 6 so it's going to be in the second quadrant so this is my x-axis that is my y-axis let's see I'm going to go negative 4 in the x-direction so 1 2 3 4 negative 4 and then 1 2 3 4 5 6 in the y-direction so the point that we care about is going to be right over there negative 4 comma 6 and they're saying what is the equation of the horizontal line it is a horizontal line so it's just going to go straight left right like this that is what the line would actually look like so what is that equation well for any X Y is going to be equal to 6 this is the equation y is equal to 6 doesn't matter what X you input here you're going to get y equals 6 it just stays constant right over there so the equation is y is equal to 6 let's do another one of these so here we are asked what is the slope of the line y is equal to negative 4 so let's visualize it and then in the future you might not have to draw it like this but let's just draw our axes again x-axis y-axis and the slope of line y equals negative 4 so for whatever X you have y is going to be negative 4 let's say that's negative 4 right over there and so the line is y the line is y equals negative 4 so I can draw it like this so what's the slope of that well slope is change in Y for given change in X and here no matter what I change my X Y doesn't change it stays at negative 4 my change in Y over change in X it doesn't matter what my change in X is my change in Y is always going to be 0 constant so the slope here is going to be equal to zero Y doesn't change no matter how much you change X let's do another one of these easier this is fun all right so now they are asking us what is the slope of the line x equals negative 3 well let me graph that one so to get them draw my axes real fast x-axis y-axis X is equal to negative 3 so negative 1 negative 2 negative 3 and so this line is going to look let me it's going to look like this no matter what Y or what you could say no matter what Y is X is going to be equal to negative 3 so it would look like this X is equal to negative 3 so what's the slope here well it's undefined a vertical line has an undefined slope remember you want to do what's your change in Y for change in X change in Y for change in X well you could think about what's the slope is you approach this but once again that could be some people would say maybe it's infinite maybe it's negative infinity but that's why it's undefined a vertical line is going to have an undefined slope so go with undefined let's do one more what is the equation of the vertical line through negative 5 comma negative 2 so let me do this one without even drawing it and then I'll draw it right after that so if we're talking about a vertical if we're talking about a vertical line that means that X doesn't change X doesn't change if we were talking about a horizontal line they would say Y doesn't change so if X doesn't change that means that X is just going to be equal to some constant value well if it contains the point negative 5 comma negative 2 so if it has the point where X is equal to negative 5 and if X never changes it's a vertical line well that means this equation has to be X is equal to negative 5 and we can draw that out if it helps so let me draw that out so let me to make sure that's a straight line okay so we have X and we have Y and so we have the point negative five comma negative two so negative one two three four five negative one two so we want to go have a vertical line that goes through that point so a vertical line well that just goes straight up and down so it's just going to look like this and so notice X never changes no matter what Y is X is equal to negative five this has an undefined slope it is a vertical line it's equation is X is equal to negative five