Writing y = mx proportional equations worked example 1 | Grade 8 (TX) | Khan Academy

We are told in a rowing exercise Claudia completes 450 strokes in 15 minutes. Write an equation that can be used to find the number of strokes y she can row in x minutes. So, pause this video and see if you can figure that out.

All right, now let's think about this together. So what I'm actually going to do is a little bit of a table here, and I'm going to put the number or I'll put time here in minutes, and this is going to be our x variable. And then over here, I'm going to put strokes, and this is going to be our y variable.

So they've already told us one that after 15 minutes—and everything here is in minutes—that Claudia was able to do 450 strokes. Is there maybe another point we can think about? Well, let's think about what happens at zero minutes. How many strokes would Claudia have done? Well, she wouldn't have done any at that point. She hadn't had a chance to do any strokes.

And so now there's something interesting going on here. We can see that when time is increasing by 15, how much are the strokes increasing by? Well, they're increasing by 450. Or another way to think about it is what is our change in y over change in x, or a change in strokes per change in time? Well, we can calculate that now. That's going to be 450 strokes for every 15 minutes.

And this we can see: 450 divided by 15 is going to be 30. And we can even write the units down—this is in strokes per minute.

Now, you might also recognize that this is the same definition as what we normally consider to be slope. So how can I write this as an equation? Well, my y, the number of strokes, is just going to be this unit rate—how many strokes per minute—which is also going to be my slope. It's just going to be that which we could consider m times x.

And you could try it out for these two points: when x is zero, y is zero; when x is 15 minutes, y is 450 strokes. And we are done.