Constant of proportionality from graph | 7th grade | Khan Academy

less than 1m read

·Nov 11, 2024

The following graph shows a proportional relationship. What is the constant of proportionality between y and x in the graph? Pause this video and see if you can figure that out.

All right, now let's do this together and let's remind ourselves what a constant of proportionality even is. If we know that there is a proportional relationship between y and x, then there will be a constant of proportionality between these variables. What this is, is it is a number that I would have to multiply x by to get to y.

So I could make a little table here, as we often do when we describe proportional relationships. X and y. We know that when x is 0, y is 0. But if I multiply 0 by anything, I'm going to get 0.

But then when x is 1, what is y? When x is 1, y is 3. They mark it right over there. When x is 2, what is y? X is 2, we see that y is 6.

So our constant of proportionality is what are we multiplying x by to get to y? Well, let's see. To go from one to three, I have to multiply by three. To go from two to six, I have to multiply by three.

Another way to think about it is we could write the equation y is equal to something times x. The number that we multiply x by to get y is our constant of proportionality. We’ve seen in all of these situations this should be true for any point on this line. You give the x, you multiply it by 3, you get your y.

So the relationship here is y is equal to 3x, so 3 is our constant of proportionality.

Comparing proportionality constants

Fuzzy Pancakes and More! LÜT #19

View All

Intelligent Species Have Only Risen Once on Planet Earth

Now that’s one argument, and we have to be humble in the face of uncertainty. Here, no one knows. But I want to give an argument that rarely gets any air time. The argument is that we are alone, and the argument has nothing to do with astronomy; it has ev…

Saddle points

In the last video, I talked about how if you’re trying to maximize or minimize a multivariable function, you can imagine its graph. In this case, this is just a two-variable function, and we’re looking at its graph. You want to find the spots where the ta…

On These Questions, Smarter People Do Worse

There is this research paper that has been on my mind for years. It shows that there is a particular type of problem where the smarter you are, the more likely you are to get it wrong. So I asked my American friend Wylie to go out on the street and ask pe…

How To Get Rich According To Grant Cardone

There are a million ways to make $1,000,000, and this is how Grant Cardone did it. Let’s just jump straight into it. Welcome to ALUX. First up, you never spend more than you earn. The principle of never spend more than you earn with a spending limit—idea…

The Side Effects of Vaccines - How High is the Risk?

Vaccines are celebrated for their part in fighting disease. But, a growing group of people seem to believe that they endanger our health, instead of protecting it. The Internet is full of stories about allergic reactions, the onset of disabilities, and ev…

Sketching exponentials

Now I want to show you a really useful manual skill that you can use when you have voltages that look like exponentials. We’re going to talk about this exponential curve here that’s generated as part of the natural response of this RC circuit. We worked …

Constant of proportionality from graph | 7th grade | Khan Academy

More Articles