Using equations and tables to represent proportional relationships
About this video
The equation y = (3/4)x has the form y = kx, so it is a proportional relationship with constant of proportionality 3/4. The video shows that y/x is always 3/4, and explains why x going up by a constant 2 in the table is not a reason for proportionality.
You'll be able to
- recognise the form y = kx as a proportional relationship.
- find the constant of proportionality from an equation.
- explain why equal steps in x do not prove a relationship is proportional.
Key words
- proportional relationship
- A relationship where y = kx, so y/x is always the same number.
- constant of proportionality
- The number k in y = kx; it equals y/x for every pair.
Transcript
- [Instructor] So, we've been given this relationship, it's expressed as an equation and as a table for certain x values. And they say which statement is true about this relationship? So pause this video, have a go at that before we do this together. Okay, before I even look at these choices, what I immediately see is that this definitely has the form of a proportional relationship.
We have y is equal to some constant times x. We're not adding or subtracting or doing anything else after that. And so it has this form y is equal to kx. Another way to think about it, if we divide both sides of this equation by x, we get y/x is equal to 3/4. So you have this constant of proportionality.
So, choice A, the relationship is proportional because y/x is always the same value. Yes, that is true. And that same value is always 3/4. So I like this one, and the other one should not. None of the other ones should be right. But let's see. The relationship is not proportional.
No, it is proportional. So let's just cross that out. The relationship is proportional. That part is true because x increases at a constant rate of two. Well, x can increase at a constant rate of two for any relationship where you could put these values that are part of the domain.
You could try x equals four or six or eight or 10 for any function, as long as those are in the domain. And that doesn't mean that they are proportional. So we'd rule that one out. The relationship is not proportional. Well, we already know what it is proportional.
So let's rule that one out as well.
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