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

Calculating slope from tables | Linear equations & graphs | Algebra I | Khan Academy


2m read
·Nov 10, 2024

We are asked what is the slope of the line that contains these points. So pause this video and see if you can work through this on your own before we do it together.

All right, now let's do it together and let's just remind ourselves what slope is. Slope is equal to change in y. This is the Greek letter delta; it looks like a triangle, but it's shorthand for change in y over change in x. Sometimes you would see it written as y2 minus y1 over x2 minus x1, where you could kind of view x1, y1 as the starting point and x2, y2 as the ending point.

So let's just pick two pairs, two xy pairs here, and we can actually pick any two if we can assume that this is actually describing a line. So we might as well just pick the first two. So let's say that's our starting point and that's our finishing point.

So what is our change in x here? We're going from two to three, so our change in x is equal to three minus two, which is equal to one. You can see that to go from two to three, you're just adding one.

And what's our change in y? Our change in y is our finishing y, one minus our starting y, four, which is equal to negative three. You could have, you didn't even have to do this math; you would have been able to see that to go from two to three, you added one, and to go from four to one, you have to subtract three.

But there we have all the information we need. What is change in y over change in x? Well, it's going to be our change in y, which is negative three, and our change in x, which is one. So our slope is negative three divided by one, which is negative three.

Let's do another example here. We are asked what is the slope of the line that contains these points. So pause this video and see if you can figure it out. Or just pause the video again and see if you can figure it out.

All right, so remember slope is equal to change in y over change in x, and we should be able to pick any two of these pairs in order to figure that out. If we assume that this is indeed a line, well, just for variety, let's pick these middle two pairs.

So what's our change in x? To go from one to five, we added four. And what's our change in y? To go from seven to thirteen, we added six. So our change in y is six when our change in x is four. And I got the signs right in both cases; it's a positive x. When x increases, y increases as well.

So our slope is 6 over 4, and we could rewrite that if we like. Both 6 and 4 are divisible by 2. So let me divide both the numerator and the denominator by 2, and we get 3 halves, and we're done.

More Articles

View All
The Adventures of a Doodlebug | A Real Bug's Life | National Geographic
After three years devouring roots in the soil, the doodlebug’s terrible transformation is complete. From greedy grub to beastly beetle. Aw, he’s kinda cute now. But don’t be fooled. He only has one thing on his mind: making more crop-destroying doodlebugs…
"Where Love Is Illegal": Chronicling LGBT Stories of Love and Discrimination (Part 2) | Nat Geo Live
I was in Lagos, Nigeria in 2014 when I heard about five young men in the north of the country who faced the death penalty for committing gay acts. They were in the Sharia Law controlled part of the country. So I went up to see them. Fortunately, by the ti…
From Startup to Scaleup | Sam Altman and Reid Hoffman
Thank you all for coming here. You’re, um, uh, everyone here is an important part of our, uh, of our joint Network. Um, this event started with a, um, kind of a funny set of accidents. First, Sam had this brilliant idea of teaching a startup class at Stan…
You Are The Center of The Universe (Literally)
A three story building is about 10 meters tall, six times bigger than you. In the opposite direction, six times smaller than you, you get things like a cute squirrel about 27 centimetres small. So the building is just as big relative to you as you are to …
The End of Robinhood..
What is up, finance alert nation? I am your host, Graham Stefan, and let’s get right into the news. Just kidding! I’m starting to feel a little bit like the drama alerts of finance lately, because we haven’t seen this much money-related drama since last w…
Nostalgia | Why Do We Mourn The Past?
People are divided about how we should approach these intense experiences related to past events called nostalgia. Some people just love to immerse themselves in memories, good or bad, and take deep journeys into the realm of the former. Other people avoi…