yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

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


2m read
·Nov 10, 2024

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.

More Articles

View All
GoodBoy3000 | Khaffeine, an audio journey by Khan Academy
[Music] Every morning, your neural chip alarm goes off at 5 a.m. metropolitan standard time. You’d prefer to be woken up by the sun, but nobody in your sector of the city is allowed to venture to the upper levels to experience real sunlight. Oh well, chip…
The Craziest Philosopher of All Time
The abstract world of philosophy is interesting. From stoicism to nihilism to absurdism, there were many different schools of thought trying to teach us how to think, act, and tell right from wrong. But have you ever felt that philosophy is sometimes a bi…
The greenhouse effect | Physics | Khan Academy
Our Earth’s surface temperature is somewhere close to 15° C—nice, cozy, and warm for us living beings. But what keeps us so warm? Well, my instinctive answer is that it’s the sun, right? But it actually gets more interesting. Our atmosphere has these gase…
How I Developed the Principled Way of Thinking
What happened is I found that I needed to write down my criteria and test them. So I started with the markets because, you know, it’s tough to wrestle all in your head with everything. I found that I needed to do that, and I could test the criteria. I fo…
Example punnet square for sex-linked recessive trait | High school biology | Khan Academy
Hemophilia is an X-linked recessive trait that affects blood clotting. If someone has hemophilia, their blood has trouble clotting. If a carrier woman and a hemophiliac man have a daughter, what is the percent chance that she, the daughter, will have hemo…
Why love and touch were once called 'dangerous' and how science proved that wrong | Nat Geo Explores
(Dramatic instrumental music) (Buzzer blares) - [TV Announcer] Never hug or kiss them. Never let them sit in your lap. Mother love is a dangerous instrument. [Narrator] Today, you’re not likely to find a popular parenting book that warns you about cuddl…