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

2m read

·Nov 10, 2024

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.

Hosain Rahman at Startup School SV 2014

Confidence intervals for the difference between two proportions | AP Statistics | Khan Academy

View All

Chase a Wild Buffalo Stampede With These Heroic Cowboys | Short Film Showcase

[Music] Big day we’re all been waiting for. Buffalo waiting; all of us are excited, a little nervous, but I guess we’re ready—ready as we’re going to be. My name is Duke Phillips. I manage the Mana Ranch. It’s um, a little over 100,000 acres located in t…

15 Reasons Why People Fail

You know, failure is something that happens to all of us at some point. It’s like running into a roadblock when you’re trying to get somewhere. What’s even more concerning is that many times we find ourselves tripping over our own shoelaces, so to speak. …

Graphing a shifted and stretched absolute value function

So we’re asked to graph ( f(x) = 2 \times |x + 3| + 2 ). And what they’ve already graphed for us, this right over here, is the graph of ( y = |x| ). Let’s do this through a series of transformations. So the next thing I want to graph, let’s see if we ca…

The Stock Market Just Flipped

What’s up, you guys? It’s Graham here. So hold on one second, I’m going to invest some money really quick. [Applause] Oops! Well, that’s basically what investing felt like this week after the inflation data came out. That’s right, in the last week we’ve …

Missing numbers in addition and subtraction | 2nd grade | Khan Academy

Let’s say someone walks up to you on the street and says, “Quick! “73 plus blank is equal to 57.” What would blank be? Well, there’s a couple of ways to think about it. Blank is essentially what you have to add to 57 to get to 73. It’s the difference be…

Warren Buffett Just Sold $100 Billion Worth of Stock.

Uh, this question is from Johan Halen, who writes, “You’re sitting on $168 billion of cash, which you told us today is now more than $182 billion.” His questions are: one, what is Buffett waiting for? And two, why not at least deploy some of it? Well, I …

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

More Articles