Drawing lines for a given slope

0:00- [Instructor] So we're told point G is graphed at the coordinates 5,3. And if we scroll down, we can see point G right over here, and it is indeed at the point 5,3. And they say, "Draw a line with a slope of 1/4 that goes through the point G." So the way I'm going to tackle this is I'll take one of these points right over here, stick it on G, and if I have a slope of 1/4, we have to just remind ourself the definition of slope.

0:30It is change in Y over change in X, or you could say rise over run. There's many ways that people talk about it, all the same thing. And so one way to think about it is the ratio between how much, if you start at a point on that line, the ratio between how much you go up and how much you go in the positive X direction is 1 to 4.

0:51So for example, if you were to go in the positive X direction by four, one, two, three, four, you would have to go up by one. So I just did what they want us to do. That is a slope of 1/4. Our rise, we've gone up one when we run when our change in X is four. But it could be any ratio like that.

1:13We could also go in the other direction. We could say, okay, if we're going down by one, if Y is going as -1, then X has to be -4. One, two, three, four. This is the same line that I just drew. I had the point over here the last time. I could also say, all right, I can increase X by eight.

1:33If I increase X by eight, let's see, 8 + 5 is 13, then I need to increase Y by two because 2/8 is 1/4. And notice, every time I drew this, it's the same line. I just have different points marked. But the first time, I marked at this point right over here at 9,4.

1:50The second time, I marked at this point right over here at 1,2. And I encourage you for all of them, look at what the change in X, look at what the change in Y over the change in X is, and you'll see it's always 1/4 between any two points on this line.