Graphing a line given point and slope | Linear equations & graphs | Algebra I | Khan Academy

We are told to graph a line with a slope of negative two that contains the point four, negative three. We have our little Khan Academy 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.

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 four, negative three. So that's, I guess you could say, the easy part. We just have to find the point four. X is four, Y is negative three. So it's from the origin: four to the right, three down.

But then we have to figure out where could another point be? Because if we can figure out another point, then we would have graphed a line. The clue here is that they say a slope of negative two. So one way to think about it is we can start at the point that we know is on the line. A slope of negative two tells us that as x increases by one, y goes down by two. The change in y would be negative two, 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 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 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 one change, or you could think of it when x has a positive one change y has a negative two 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 one and y going down by 2. It's the exact same line.