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## Constant of proportionality

## Video transcript

- [Instructor] We are
asked, "What is the constant "of proportionality in the
equation 4y is equal to 8x?" Pause this video and have
a go at this question. All right, so we might be used to seeing constants of proportionality when we have equations in
a slightly different form. A constant of proportionality is what do you multiply x by to get to y? So y would be equal to our constant of
proportionality times x. But this isn't written in that form, so what we do is
manipulate it a little bit so that we can see it in that form. And the obvious thing is we
just need to solve for y. So right now it says 4y is equal to 8x. Well, if we wanna solve for y, we can just divide both sides by four, and we are left with y is
equal to eight divided by four, which is two times x. Well, now the constant of
proportionality jumps out at us. To get y, we have multiply x by two. That is our constant of proportionality. Let's do another example. Here we're asked, "Which
equation has a constant "of proportionality equal to 1/2?" Again, pause the video. Try to answer it yourself. Okay, so I'm just gonna
go equation by equation and calculate their
constants of proportionality and see which one has a constant of proportionality equal to 1/2. So this one right over here,
choice A clearly has a constant of proportionality of 1/8,
so we can just rule that out. Equation B right over here
clearly has a constant of proportionality of four, not 1/2, so we can rule that one out. Let's see, the constant of
proportionality for equation C, if we wanna solve for y, we
could divide both sides by six. And so we're gonna get y
is equal to 3/6 times x. Well, 3/6 is the same
thing as 1/2 times x, and so there you have it. We have a constant of
proportionality of 1/2. That's the choice I like. And we can verify that
this one doesn't work. If you wanna solve for y, you
divide both sides by three, and you get y is equal to
nine divided by three is 3x, so here our constant of
proportionality is three, so we can feel good about choice C.