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a line is graphed and the XY plane is shown which of the following equations represents the line they give us a bunch of equations here and so there's a several ways we can tackle it when we look at this I could see there's two interesting points here there's the point when X is let me just write this and actually me write a little lower so we can look at it at the same time that I look at the equation choices so we see that when X is zero Y is one so that is the y intercept we could say and then when you can see when X is 6 Y is zero when X is 6 Y is zero so a very kind of basic way of approaching this is see like well but when X is zero Y needs to be equal to 1 when X is zero we get 6 y is equal to 1 well then Y is going to be equal to 1/6 rule that one out when X is equal to 0 Y needs to be equal to 1 if X is 0 then 6 y equals 6 yea Y is going to be equal to 1 now when y is 0 X is going to be X needs to be equal to 6 so if Y is 0 this goes away and X is equal to 6 so we're done this is our choice now there's other ways that we could do it we could write it first in slope intercept form and then convert to this form right over here so let's do it that way as well so we could say that the equation of this line is going to be Y if I write it in y equals MX plus B form where m is the slope and B is the y-intercept we already know that B is equal to 1 so we already know that's 1 and what's the slope well slope is our change in Y for given change in X and we see when our when our change in X is positive 6 when our change in X is positive 6 our change in Y is negative 1 so our slope is we decrease in Y by 1 when we increase in X by 6 is negative 1/6 so the equation of the line y is equal to negative 1/6 X this is the slope plus 1 and then we could convert to the forms that we have here so let's see we could add and we could add 1/6 X to both sides you're gonna get one over 6x plus y is equal to one and that's not quite what we have here all over here all the X coefficient or the coefficients on X are just one so we could multiply both sides of this time six and we would get X plus 6y is equal to six which is exactly the choice that we picked