Ratios on coordinate plane

We are told that a baker uses eight cups of flour to make one batch of muffins for his bakery. Complete the table for the given ratio. So they're saying that for every batch, he needs eight cups of flour, or he needs eight cups of flour for every batch.

Sofini had two batches. How many cups of flour would that be? Pause the video and try to figure it out. Well, if he has twice as many batches, he's going to have twice the number of cups of flour. So instead of 8, it would be 16 cups of flour.

And if you had 3 times the number of batches, it would be 3 times the number of cups of flour. So instead of 8, it would be 8 times 3, or 24.

Now down here, they say plot the ordered pairs (x, y) from the table on the following graph. So we want to graph one batch, eight cups; two batches, 16 cups; three batches, 24 cups.

So let's do that. So let's see if you can. Okay, so right here, this I'm assuming on the horizontal axis, that is our batches, and then our vertical axis is cups of flour. So for every batch, we need eight cups of flour. So one batch, this is eight right over here: five, six, seven, eight.

And then for two batches, we're going to need 16 cups of flour, so that puts us right over there; that's 16. And then for three batches, we are going to need 24 cups of flour, and that actually goes slightly off of our screen here.

Let me scroll up a little bit. So for three batches, we are going to have to bring that to 24, which is right here. And I can see the 25 right above that. What you'll see, because the ratio between our batches and our cups of flour are constant, is that all of these points you could connect them all with one straight line.

Because we have a fixed ratio, every time we move one to the right, we're going to move eight up. Every time we add another batch, we're going to have eight more cups of flour. Every time we add a batch, eight more cups of flour.

Let's do another example here. We're told Drew earns money washing cars for his neighbors on the weekends. Drew charges a set rate for each car he washes. The points on the following coordinate plane show how much Drew charges for two, five, and eight cars.

So let's see what's going on over here. So when he washes two cars, it looks like he charges fifteen dollars. When he washes five cars, it looks like he's charging, well, it looks like someplace between 35 and 40 dollars. And he charges eight cars; it looks like he's charging sixty dollars.

So one way to think about it is the ratio between the number of cars he's washing and the dollars. It stays at two to fifteen. Notice two cars for every fifteen dollars. I guess I could say fifteen dollars for every two cars. And so when you go to eight cars, you're multiplying by four the number of cars, and you're also multiplying by four the number of dollars.

And so once again, since we have a fixed ratio here, all three of these points sit on the same line. But then they ask us down here, they say how much does Drew charge for four cars? Well, if it's fifteen dollars for two cars, well, then four cars would be twice as much, so it would be thirty dollars for four cars. We have the same ratio.

Let's do one more example here. We're told McKenna earns money each time she shovels snow for her neighbors, as she should. McKenna plots points on the coordinate plane below to show how much she earns for different numbers of times she shovels snow.

All right, so let's see. When she shovels snow three times, it looks like she gets, see, halfway between 16 and 20. Looks like she gets 18. Four times, look, it's 24. So it looks like the ratio is staying constant at 3 to 18.

The ratio of 3 to 18 is the same thing as—one way to think about it is 18 for every three times she shovels snow. That'd be equivalent to six dollars for every time she shovels snow.

So let's go down here to see what they're asking us. They say, which of the following ordered pairs could McKenna add to the graph? So this would be one time shoveling snow. Would she get ten dollars for it?

So does she get ten dollars for every time she shovels snow? No, that wouldn't be consistent with the data here. She got eighteen dollars for shoveling snow three times, so that looks like she's getting six dollars for every time she shovels snow. So I would rule out choice A.

Choice B: Shoveling snow twice, she gets 12. Well, that makes sense. If she gets six dollars every time she shovels snow, if the ratio of the times shoveling to the dollars is 3 to 18, or 1 to 6, that would be equivalent to 2 to 12, and we would pick that choice.