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
Free energy of dissolution | Applications of thermodynamics | AP Chemistry | Khan Academy
The term dissolution refers to the dissolving of one substance in a solvent. The dissolved substance is now called a solute, and the solute plus the solvent form a solution. If the standard change in free energy, delta G naught, is less than zero, the dis…
The U.S. Interest Rate Problem Just Flipped (Jerome Powell Changes Stance)
If you’ve been paying attention to the stock market recently, you’ll have noticed it’s currently nose diving. It’s nothing crazy yet; it’s definitely not a stock market crash. But the S&P 500 is down around 5% since just last week. If you’re wondering…
Watch the Total Solar Eclipse | National Geographic
Hello everyone and welcome to this momentous day. It is the Great American Eclipse day and we’re here with National Geographic and Airbnb on this live stream on Facebook, YouTube, and Periscope. My name is Cara Santa Maria and I am a science communicator.…
The Mummification of Seti I | Ultimate Treasure Countdown
[music playing] NARRATOR: Seti the First was the father of our friend Ramesses the Great. Just like his son, he was a hugely successful pharaoh. But in father-son rivalry, there’s one category where he wins hands down: his mummy. Because Seti the First b…
The Archer's Paradox in SLOW MOTION - Smarter Every Day 136
Hey, it’s me Destin, welcome back to Smarter Every Day. So in one of the last episodes, I introduced you to a legend with a longbow. He’s from my hometown and his name is Byron Ferguson. He shot an aspirin out of the air in slow motion. But there’s someth…
Why Science Says It's Good for Kids to Lie | National Geographic
[Music] My name is Ellen. I’m a research assistant at Kong Leaf Development Lab. This is where we do our deception studies, and here we play three games with the kids. You’ve been doing such a good job, and we got off to such a good start that I kind of w…