yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Constant of proportionality from equation


2m read
·Nov 11, 2024

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.

More Articles

View All
Peter Lynch: How to Invest for Beginners (7 Investing Rules)
I’m amazed how many people own stocks; they would not be able to tell you why they own it. They couldn’t say in a minute or less why they don’t. Actually, if you really pressed them down, they’d say, “The reason I own this is the sucker’s going up,” and t…
Jim Crow part 4 | The Gilded Age (1865-1898) | US History | Khan Academy
So we’ve been talking about the system of Jim Crow segregation. In the last video, we left off in 1876. In 1876, there was a contested presidential election between a Republican candidate named Rutherford B. Hayes and a Democratic candidate named Samuel J…
The Secret to Building Wealth Fast
What if we told you there was a way to build extreme levels of wealth incredibly fast? What if we told you that almost all self-made millionaires and billionaires have used this exact strategy to build their fortunes? And there’s nothing stopping you from…
Rulings on majority and minority rights by the Supreme Court | Khan Academy
We’ve already talked about the 14th Amendment in previous videos, but just as a reminder, Section 1 of the 14th Amendment says, “All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United Stat…
Work is the set of things that you have to do, that you don't want to do
What would you say the key differences are between success and failure? What does one startup have versus one that doesn’t make it? Uh, luck is a big one. Timing is everything, but you kind of make your own luck, you know, if you stay at it long enough. …
Welcome to Atlantium, the Nation Formed in a Backyard | Short Film Showcase
The purpose of Atlantium is to give people a vision of how a globalized world could properly function, in which everyone has the possibility of realizing the fullness of their personal potential. What do you do if you don’t like the country you were born…