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

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.