Relating unit rate to slope in graphs of proportional relationships
Narrator says '28 kilograms' at about 72s, then corrects it to 26 kilograms at about 80s. Interventions use 26.
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A farmer sells 26 kilograms of tomatoes for $78, and the video finds which graph has a slope equal to the cost in dollars per kilogram. Slope is change in y over change in x, so here it is dollars divided by kilograms: 78/26 = $3 per kilogram. The correct graph is the one where dollars go up by 3 every time kilograms go up by 1.
You'll be able to
- explain that slope is change in y divided by change in x.
- find a unit rate such as dollars per kilogram from a total cost and a total amount.
- pick the graph whose slope matches a given unit rate.
Key words
- slope
- How much y changes for each change in x: change in y divided by change in x.
- unit rate
- How much of one quantity there is for exactly one unit of another, like $3 per kilogram.
- per kilogram
- For each single kilogram.
Transcript
- [Instructor] A farmer sold 26 kilograms 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, x is the weight in kilograms. So what we really want to do is, we wanna take the total cost, because that's what our vertical axis here, 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, $78 for every 26 kilograms. They sold 26 kilograms and it sold it for $78.
So for 28 kilograms. And we can see that our units are right. It's in dollars per kilogram. It says in dollars per kilogram. So what is, I'm sorry, that's 26 kilograms. I may not make a mistake. 26 kilograms. So what is 78 divided by 26? Well, 78 is exactly three times 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. It's essentially, have a slope of three. Every time the kilogram increases by one, our dollars 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 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 increased by four, so I will also rule that one out. So I like this choice right over there.
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