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

Identifying proportional relationships from graphs | 7th grade | Khan Academy


2m read
·Nov 11, 2024

We are asked how many proportional relationships are shown in the coordinate plane below, and we have the choices. But let's actually look at the coordinate plane below to think about how many proportional relationships are depicted here. So pause this video and try to answer that yourself.

So let's do this together. If we're thinking about a proportional relationship or the graph of a proportional relationship, there should be two things that we're looking for. One, it should be a line; it should be a linear relationship between the two variables. Y should be some constant, some proportionality constant times X.

So you immediately would rule out our green curve here because this is not a line. You don't have a constant relationship between Y being some proportionality constant times X. And for the same reason, you would rule out this blue curve.

Now what about this purple line? This might be tempting because it is a line, but it does not go through the origin. When X is 2, Y is 0 times X, while when X is 4, Y is 1 times X, and when X is 6, Y looks to be 1 1/3 times X. So you don't have the same proportionality constant the entire time. So we have zero proportional relationships depicted here, so I would pick 0 there.

Let's do one more example. Natalie is an expert archer. The following table shows her scores (points) based on the number of targets she hits. All right, targets hit and then the points she gets. Plot the order pairs from the table.

All right, so the first one is (1, 3). So here I'm doing it on Khan Academy. My horizontal axis is targets hit, and my vertical axis is points. So one target hit, three points. So this is going to be one target hit; this is going to be three points.

Then I have two targets hit, six points. So two targets hit, and I have six points. And then I'm gonna have three or five targets hit, 15 points. So then I'm going to have, going to have five targets hit, and that is going to be 15 points.

And so this is looking like a proportional relationship in every situation. My point is equal to three times the targets hit, so my proportionality constant is three. And you can see if you try to connect these dots with a line, it will be a line. A line can go through all three of these, and it will go through the origin.

So are Natalie's points proportional to the number of targets she hit? Yes, absolutely.

More Articles

View All
My Advice For Trump and Harris With Two Weeks Left
TR Trump is Trump. People know him. Um, they’ve been listening to him for over, you know, seven years. They know exactly how he is. He’s no filter. However, he comes across as being very authentic. 45% of people hate him in America. 45% of people love hi…
Are We Running Out of Sand?
[Music] It can be easy to take something for granted that every time you see it, it seems to go on forever. It’s like an infinite path to the horizon, a landscape that never ends. This is sand. And even though just a simple trip to the beach can make it f…
Adventurers Jim & Tori Baird on their son’s FOXG1 diagnosis, life in the wild | National Geographic
Wesley, as challenging as some of our days might be with him, I wouldn’t want to change him for the world because he is just the happiest little thing. My name is Jim Baird and I am Tori Baird. We have two boys, Wesley and Hudson. Wesley is just a little…
Motion problems with integrals: displacement vs. distance | AP Calculus AB | Khan Academy
What we’re going to do in this video is start thinking about the position of an object traveling in one dimension. To get our bearings there, I’m going to introduce a few ideas. So the first idea is that of displacement. You might use that word in everyd…
The Wolf of Wall Street (Movie Commentary W/ @HamishHodder and Jason Hughes)
Maybe live right now and we’re on one second, two seconds, three. So, how we going, gents? Welcome in. Hey, Miss Jason, what’s cracking? Not a lot, going well? Yeah, good stuff here. Hey, we’ve got some COVID up here. Oh yeah? Yeah, that’s, you’re in Syd…
Visually dividing decimal by whole number
In this video, we’re going to try to figure out what 4 tenths divided by 5 is. So pause this video and see if you can think about it before we work through it together. We’re really going to think about approaching this visually. All right, now let’s wor…