Relating unit rate to slope in graphs of proportional relationships | Grade 8 (TX) | Khan Academy

A farmer sold 26 kg of tomatoes for $78. Which graph has a slope that represents the cost of tomatoes in dollars per kilogram?

Pause this video, work through this on your own before we do this together.

So, if we're thinking about slope, slope is all about the change in the vertical axis divided by the change in the horizontal axis. Sometimes you see slope is equal to change in y over change in x. In this case, we could say y is the cost in dollars and x is the weight in kilograms.

What we really want to do is we want to take the total cost because that's what our vertical axis is for. That's what we're measuring in y. So, this is going to be the cost per the number of tomatoes, or I should say the weight of the tomatoes because that's what the horizontal axis is for—the weight.

And they give us that it's going to be $78 for every 26 kg they sold. So, for 26 kg, it cost $78. So, for 1 kg, we can see that our units are right; it's in dollars per kilogram. It says in dollars per kilogram.

So, what is—sorry, that's 26 kilograms, not to make a mistake—26 kilograms. So, what is 78 divided by 26? Well, 78 is exactly 3 * 26. So, I could rewrite this as $3. Actually, let me write it this way: $3 per kilogram.

So, that's what the unit price is—how much the farmer is getting per kilogram of tomatoes.

So, let's see which of these slopes match up to that. Essentially, we have a slope of three. Every time the kilogram increases by one, our dollar should increase by three.

This one clearly is not the case; when kilograms increase by one, dollars are increasing by one. So, I'll rule this one out.

This one, every time kilograms increase by one, dollars looks like they're increasing by 1/3. So, I'll rule this one out.

Here, every time the kilogram increases by one, it looks like dollars are increasing by three. This one looks right; I will check that box.

Here, it looks like every time we increase kilograms by one, our dollars increase by four. So, I will also rule that one out.

So, I like this choice right over there.