About this video
When an equation isn't written as y = kx, you can solve for y to see the constant of proportionality. The video turns 4y = 8x into y = 2x (constant 2), then checks several equations to find the one with constant 1/2: 6y = 3x becomes y = 3/6 x = 1/2 x, while 3y = 9x becomes y = 3x.
You'll be able to
- rewrite an equation like 4y = 8x in the form y = kx by dividing both sides.
- find the constant of proportionality from an equation in any form.
- compare several equations to find the one with a given constant.
Key words
- constant of proportionality
- The number you multiply x by to get y, the k in y = kx.
- solve for y
- Rearrange an equation so y is by itself on one side.
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.
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