Calculating slope from tables (video) | Khan Academy

Video transcript

– [ Instructor ] We are asked, what is the slope of the line that contains these points ? so pause this television and see if you can work through this on your own before we do it together. Alright, now let ‘s do it together, and let ‘s just remind ourselves what gradient is. Slope is peer to change in yttrium, this is the greek letter delta, look likes a triangle, but it ‘s shorthand for change in yttrium over change in x. sometimes you would see it written as y2 minus y1 over x2 minus x1 where you could kind of opinion x1 y1 as the starting compass point and x2 y2 as the ending point. So let ‘s merely pick 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 adenine good just pick the first two. So let ‘s say that ‘s our depart point and that ‘s our coating sharpen. So what is our change in adam here ? So we ‘re going from two to three, so our change in adam is equal to three minus two which is equal to one, and you can see that to go from two to three you ‘re just adding one. And what ‘s our change in yttrium ? Our change in yttrium is our finishing y one subtraction our starting yttrium four, which is peer to negative three. And you could of, you didn’t even have to do this mathematics, you would have been able to see to go from two to three you added one, and to go from four to one, you have to subtract three. For there we have all the information we need. What is change in yttrium over change in x ? Well, it ‘s going to be, our exchange in y is minus three and our change in ten is one. So our slope is negative three divided by one is negative three. Let ‘s do another case. here we are asked, what is the slope of the line that contains these points ? sol pause this television and see if you can figure it out or pause the video recording again and see if you can figure it out. Alright, so remember, slope is equal to change in y over change in ten. And we should be able to pick any two of these pairs in regulate to figure that out if we assume that this is indeed a line. Well, good for variety show, let’s pick these in-between two pairs. So what ‘s our deepen in adam ? To go from one to five, we added four. And what ‘s our change in yttrium ? To go from seven to 13, we added six. sol our change in yttrium is six when our switch in x is four. And I got the signs mighty, in both case it ‘s a positivist. When ten increases, yttrium increased vitamin a well. sol our slope is six fourths, and we could rewrite that if we like. Both six and four are divisible by two, so let be divide both the numerator and the denominator by two and we get three halves, and we ‘re done.

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