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CCSS.Math: , , ,

we are asked to graph y is equal to one-third X minus 2 now whenever you see an equation in this form this is called slope-intercept form and the general way of writing it is y is equal to MX plus B where m is the slope and here in this case M is equal to 1/3 so let me write that down M is equal to 1/3 and B is the y-intercept so in this case B is equal to negative 2 B is equal to negative 2 and you know that B is the y-intercept because we know that the y-intercept occurs when X is equal to 0 so if X is equal to 0 and either of these situations this term just becomes 0 and Y will be equal to B so that's what we mean by B is the y-intercept so whenever you look at an equation in this form it's actually fairly straightforward to graph this line B is the y-intercept in this case it is negative 2 so that means that this line must intersect the y-axis at Y is equal to negative 2 so it's this point right here negative 1 negative 2 this is the point 0 negative 2 if you don't believe me there's nothing magical about this try try evaluating or try solving for y when x is equal to 0 when X is equal to 0 this term cancels out and you're just left with Y is equal to negative 2 so that's the y-intercept right there now this 1/3 tells us the slope the slope of the line how much do we change in Y for any change in X so this tells us that 1/3 so that right there is the slope so it tells us that 1/3 is equal to the change in Y over the change in X over the change in X or another way to think about it if X changes by 3 then Y will change by 1 so let me graph that if X change so we know that this point is on the graph that's the y-intercept the slope tells us that if X changes by 3 so let me go three to the right one two three that Y will change by one y will change by one so this must also be a point on the graph and we could keep doing that if X changes by three Y changes by one if X goes down by three if X goes down by three Y will go down by one if X goes down by six y will go down by two it's that same ratio so one two three four five six one two and you can see all of these points are on the line and the line is the graph of this equation up here so let me graph it let me graph it so it'll look something like it will look something like something like that and they're done