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

Interpreting graphs of proportional relationships | 7th grade | Khan Academy


2m read
·Nov 11, 2024

  • [Instructor] We are told the proportional relationship between the number of hours a business operates and its total cost of electricity is shown in the following graph. All right. Which statements about the graph are true? Choose all answers that apply. So pause this video and see if you can figure this out.

All right, now let's do this together. And before I even look at the choices, let me analyze this a little bit. It is a proportional relationship. So we know that our total cost, let me write it here, our total cost is going to be equal to some constant of proportionality times our number of hours.

And we can even figure out what that constant of proportionality is going to be, because they give us this point A. We know that when our hours are four, so when this is four right over here, our total cost is $120. $120. So what times four is equal to 120? Well, we know that this k must be 30, 'cause 30 times four is 120.

So we can write that proportional relationship where our total cost is going to be equal to our constant of proportionality, 30, times our number of hours. Number of hours. So let's see which of these choices, and it might be more than one, say this or describe what's going on here.

So choice A, the y-coordinate of point A, so point A is at the point four comma 120, so the y-coordinate is the 120. That's the total cost when you run your business for four hours. The y-coordinate of point A represents the total cost of electricity when the business operates for four hours. Yes, that is exactly or very close (laughs) to what I just said, so I like this one.

The total cost of electricity is $35 when operating the business for one hour. So let's go to one hour here. This is going to be the total cost. Now, you might say, hey, this looks kinda close to $35, but that's why it was useful for us to write this relationship right over here, because what we see is that our total cost is going to be 30 times our number of hours.

Our total cost here is actually going to be 30, not 35. And it actually does look smack dab in between 20 and 40 versus a little bit closer to 40. So this one is not going to be true. And we're not gonna select none of the above, 'cause we actually did select one of the above. And we're done.

More Articles

View All
Constructing exponential models: percent change | Mathematics II | High School Math | Khan Academy
Cheppy is an ecologist who studies the change in the narwhal population of the Arctic Ocean over time. She observed that the population loses 5.6% of its size every 2.8 months. The population of narwhals can be modeled by a function n, which depends on th…
The WALKING WATER Mystery (in SPACE and SLOW MOTION!) - Smarter Every Day 160
Hey, it’s me Destin and welcome back to Smarter Every Day! I have a problem. There is a specific water phenomenon that I see happening all around me, but I have no idea how it works. I’ve been trying to figure it out for years. In fact, I put a video on t…
High Speed Fun and a Fly Responding to a Blast Wave | Smarter Every Day 55
Hey it’s me Destin, welcome back to Smarter Every Day. So I am in the middle of the California desert and the sun is setting, and it’s beautiful, so I’ll just let you see that while I set this video up for you. So a guy named Jeff, he’s taofledermaus on …
How To Go From Startup Dream To Reality
There’s a moment in a Founder’s brain when you know your startup is gonna die. You see the future, but the future is looking like darkness. In the movie Encanto, there’s a magical character named Bruno who can tell the future, but it’s always bad news. W…
Ray Dalio on his Principles for Success
Can you think about, like, what are some of your first principles? Life is a journey. It’s an adventure, an adventurous journey in which you come into it with having a certain nature. That nature, um, you’re in a journey to find the path to match up with …
The FED Just Crashed The Market | Major Changes Explained*
What’s up guys, it’s Graham here. So, as of a few hours ago, the Federal Reserve just raised their benchmark interest rates by another 75 basis points, which means as of today we are now sitting at the highest interest rates that we’ve seen since 2008. Th…