Writing y = mx proportional equations worked example 1
About this video
Claudia rows 450 strokes in 15 minutes, and the video writes an equation for the strokes y she rows in x minutes. Using a table with the points (0, 0) and (15, 450), the unit rate is 450/15 = 30 strokes per minute, which is also the slope m. The equation is y = 30x, which works for both points.
You'll be able to
- find a unit rate from a word problem and give its units.
- explain that the unit rate is the slope m in y = mx.
- write and check a proportional equation y = mx.
Key words
- unit rate
- The amount for one unit, such as 30 strokes per minute.
- slope
- Change in y divided by change in x; in y = mx it is the number m.
- proportional relationship
- A relationship of the form y = mx, where y is always the same multiple of x.
Transcript
- [Instructor] 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. Alright, now let's think about this together.
So what I'm actually gonna 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 gonna 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 our 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 45 divided by 15 is 3. So 450 divided by 15 is going to be 30. And we could even write the units down. This is in strokes per minute, 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.
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