Constant of proportionality from equation

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, 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.

The obvious thing is we just need to solve for y. So, right now it says 4y is equal to 8x. Well, if we want to solve for y, we can just divide both sides by 4, and we are left with y is equal to 8 divided by 4, which is 2 times x. Well, now the constant of proportionality jumps out at us; to get y, we have to multiply x by 2. That is our constant of proportionality.

Let's do another example here. We're asked which equation has a constant of proportionality equal to one-half. Again, pause the video, try to answer it yourself.

Okay, so what we—I'm just going to go equation by equation and calculate their constants of proportionality and see which one has a constant of proportionality equal to one-half. 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 4, not 1/2, so we could rule that one out.

Let's see the constant of proportionality for equation C. If we want to solve for y, we could divide both sides by 6. And so we're going to get y is equal to 3/6 times x. Well, 3/6 is the same thing as one-half times x, and so there you have it; we have a constant of proportionality of one-half. That's the choice I like.

We can verify that this one doesn't work. If you divide—if you want to solve for y, you divide both sides by 3 and you get y is equal to 9 divided by 3, which is 3x. So here, our constant of proportionality is 3, so we can feel good about choice C.