Analyzing proportionality using equations and tables: distance
The narrator says 'concept of proportionality' instead of 'constant of proportionality' when reading a choice; the meaning is clear from context.
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The equation c = 100m, linking centimeters and meters, has the form y = kx, so the relationship is proportional with constant of proportionality 100. The video uses it to fill in a table and rule out wrong choices like 30 cm in 3 m or adding 100 + 4.
You'll be able to
- recognise c = 100m as a proportional relationship.
- identify the constant of proportionality in an equation.
- use the equation to convert meters to centimeters.
Key words
- proportional relationship
- A relationship where one quantity is always a constant times the other, like c = 100m.
- constant of proportionality
- The constant k in y = kx; here k = 100 because c/m is always 100.
- dependent variable
- The quantity that depends on the other; here the centimeters c.
Transcript
- [Instructor] We are told the equation c equals 100m describes the relationship between the distance in centimeter, c, and the distance in meters, m. Jaya uses a table below to help decide whether there's a proportional relationship between centimeters and meters, all right?
Which two conclusions can Jaya correctly make about the relationship? So pause this video, have a go at this before we do it together. Okay, so we could either just think about it a little bit and then look at the choices or go vice versa. Actually, let me just think about it before I look at the choices.
That's what I like to do when I'm taking any kind of an assessment or answering a question. So immediately when I see that c is equal to 100m, I can think of this as this is just like saying c is equal to some constant times m, which is one way, one pattern for looking at proportional relationships.
Another way to think about it is, if I were to divide both sides by m, I would get c divided by m is equal to 100. And whenever you have this, where you have the dependent variable divided by the independent variable is equal to a constant number, in this case the k is 100, that is also a proportional relationship.
And here they're also putting it in a table here. I mean, we could say that this question mark right over here would be 300. This question mark right over here would be 400. We're just multiplying whatever is in meters times 100. But anyway, let's see what the answers are.
What can be true? They're 30 centimeters in, in three meters. 30 centimeters, no, we just said there are 300 centimeters in three meters. You take your meters, you multiply by 100. That's what this equation told us. The concept of proportionality between c and m is 100.
Yeah, we got that right over here, or we looked at it over here, so I like that one. The relationship between c and m is proportional. Yes, I like that one too. We had already come to that conclusion. And so this one should be wrong, this last one, because it says choose two answers.
To find the number of centimeters in four meters, add 100 plus four. No, you would take the meters, multiply by 100, and get centimeters. You would do 100 times four. So this one was wrong as well.
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