Graphing a line given point and slope

we are told graph a line with the slope of negative two that contains the point 4 comma negative 3 and we have our little khanacademy graphing widget right over here where we just have to find two points on that line and then that will graph the line for us so pause this video and even if you don't have access to the widget right now although it's all available on Khan Academy see how you would think at least think about how you would approach this and if you have paper and pencil handy I encourage you to try to graph this line on your own before I work through it with this little widget all right now let's do it together so we do know that it contains the point 4 comma negative 3 so that's I guess you could say the easy part we just have to find the point 4 X is 4 y is negative 3 so it's from the origin 4 to the right 3 down but then we have to figure out well where could another point be because if we can figure out another point then we would have graphed a line and the clue here is that they say a slope of negative 2 so one way to think about it is we can start at the point that we know is on the line and a slope of negative 2 tells us that as x increases by 1 Y goes down by 2 the change in Y would be negative 2 and so this could be another point on that line so I could graph it like this as X goes up by 1 as X goes from 4 to 5 Y will go or Y will change by negative 2 so Y will go from negative 3 to negative 5 so this we would be done we have just graphed that line now another way that you could do it because sometimes you might not have paid space on the paper or on the widget to be able to go to the right for X to increase is to go the other way if you have a slope of negative 2 another way to think about it is if X goes down by one if X goes down by 1 then Y goes up by 2 because remember slope is change of Y over change in X so you could either say you have a positive change in Y of 2 when X has a negative 1 change or you can think of it when X has a positive 1 change Y has a negative to change but either way notice you got the same line notice this line is the same thing as if we did it the first way as we had X going up by 1 and Y going down by 2 it's the exact same line