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

Locating less obvious y-intercepts on graphs | Grade 8 (TX TEKS) | Khan Academy


3m read
·Nov 10, 2024

So we have the graph of a line shown right over here, and my question to you is: what is the Y intercept of this line? Pause this video and see if you can figure it out yourself.

All right, now let's work through this together. So when we just eyeball it over here, we can see that the Y intercept, which is where the line intersects the Y axis, is right about there. It's between two and three, but we don't know what it is exactly, so we're going to have to do a little bit of algebra.

You might already remember that the equation of a line can be expressed as Y is equal to mx + b, where m is the slope and b is the Y intercept. So what we're going to do is use these two points they've given us to first figure out the slope of this line and then figure out the Y intercept, and then we will be done.

So let's figure out the slope. Slope, you might remember, is change in y over change in x. Now, we could do this two ways. It looks like you could eyeball this maybe, but I'll confirm this using actual numbers. If I go from this point, which looks like the point (4, 0), to this point right over here, it looks like our change in y is -2 when our change in x is positive 3. So change in y over change in x is -2/3.

Another way, just to make sure that I'm not eyeballing it incorrectly, is I could look at these two points which they've actually given us the coordinates for: change in y over change in x. From this point (-2, 4) to this point (7, -2), I could say my change in y is this y value (-2) minus this y value (4) over, and I didn't really need the parentheses there, over this x value (7) minus this x value (-2).

So this is going to be equal to, let's see: -2 - 4 is -6, and then 7 - -2 is the same thing as 7 + 2, which is 9. Which is, once again, -6/9, which is -2/3.

So we know that this equation has the form—let’s do this another color—Y is equal to (-2/3)x + b. Now, to solve for b, I could just substitute one of these points in here for x and y and just solve for b. I usually try to pick whichever one the math might be a little bit easier. They're close, but I'll go with this one.

So when x = -2, y is equal to 4. So let me substitute that in here. So y is equal to four, so 4. I just substitute this y with 4, is equal to (-2/3) times x, so times -2 plus b.

And so let’s see: this is 4 is equal to (-2/3) times -2, which is going to be positive 4/3 plus b. Now, if I want to solve for b, I could subtract 4/3 from both sides, and I will get b is equal to 4 minus 4/3.

All I did here is I subtracted 4/3 from both sides, and I swapped the two so I could put b on the left just because I like how that looks. And so this is going to be the same thing. Four, if I express it as thirds, is the same thing as 12/3 minus 4/3, which is equal to 8/3.

And 8/3 is the same thing as, let me scroll down a little bit, it's the same thing as, let's see, three goes into eight two times with the remainder two, so it's two and 2/3, which is exactly what it looks like we have right over here. Our Y intercept right over there is at 2 and 2/3. 2 and 2/3, and we're done.

More Articles

View All
Zero-order reactions | Kinetics | AP Chemistry | Khan Academy
Let’s say we have a hypothetical reaction where reactant A turns into products. Let’s say the reaction is zero order with respect to A. If it’s zero order with respect to A, we can write that the rate of the reaction is equal to the rate constant k times …
Newton's first law | Physics | Khan Academy
You’re standing in a bus at rest, without any support. Suddenly, the bus starts moving, and you fall back, as if someone pushed you back. Why does this happen? You get back on your feet, and now suddenly the bus stops, and you fall forward, as if someone …
Mark Zuckerberg On Yahoo's Billion Dollar Offer
I want to talk for a second about low points because I think people never appreciate how bad they really are. I think it’s always reassuring to hear that even Mark Zuckerberg went through some serious low points and came out okay. So, can you tell us abo…
More Compute Power Doesn’t Produce AGI
The artificial general intelligence crew gets this completely wrong too. Just add more compute power and you’ll get intelligence when we don’t really know what it is underneath that makes us creative and allows us to come up with good explanations. Peopl…
Economic profit for a monopoly | Microeconomics | Khan Academy
In this video, we’re going to think about the economic profit of a monopoly firm. To do that, we’re going to draw our standard price and quantity axes. So, that’s quantity and this is price, and this is going to of course be in dollars. We can first thin…
How Much I Make With 3 Million Subscribers
What’s up you guys! It’s Graham here. So I’m sure at some point you’ve been scrolling YouTube. You come across your favorite creator, and then you start to think to yourself, “How much money are they making?” No? Just me? Alrighty then! I’ll end the vide…