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- [Instructor] We are asked,

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what is the slope of the line[br]that contains these points?

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So pause this video and see[br]if you can work through this

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on your own before we do it together.

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Alright, now let's do it together,

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and let's just remind[br]ourselves what slope is.

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Slope is equal to change in y,

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this is the Greek letter delta,

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look likes a triangle,

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but it's shorthand for change in y

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over change in x.

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Sometimes you would see[br]it written as y2 minus y1

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over x2 minus x1

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where you could kind of view[br]x1 y1 as the starting point

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and x2 y2 as the ending point.

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So let's just pick two xy pairs here,

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and we can actually pick any two

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if we can assume that this is[br]actually describing a line.

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So we might as well[br]just pick the first two.

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So let's say that's our starting point

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and that's our finishing point.

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So what is our change in x here?

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So we're going from two to three,

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so our change in x is[br]equal to three minus two

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which is equal to one,

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and you can see that[br]to go from two to three

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you're just adding one.

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And what's our change in y?

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Our change in y is our finishing y one

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minus our starting y four, which[br]is equal to negative three.

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And you could of, you didn't[br]even have to do this math,

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you would have been able to see

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to go from two to three you added one,

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and to go from four to one,[br]you have to subtract three.

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For there we have all[br]the information we need.

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What is change in y over change in x?

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Well, it's going to be,

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our change in y is negative three

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and our change in x is one.

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So our slope is negative[br]three divided by one

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is negative three.

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Let's do another example.

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Here we are asked, what is the slope

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of the line that contains these points?

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So pause this video and see[br]if you can figure it out

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or pause the video again and[br]see if you can figure it out.

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Alright, so remember, slope[br]is equal to change in y

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over change in x.

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And we should be able to[br]pick any two of these pairs

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in order to figure that out if we assume

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that this is indeed a line.

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Well, just for variety, let's[br]pick these middle two pairs.

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So what's our change in x?

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To go from one to five, we added four.

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And what's our change in y?

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To go from seven to 13, we added six.

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So our change in y is six[br]when our change in x is four.

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And I got the signs right,[br]in both case it's a positive.

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When x increases, y increased as well.

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So our slope is six fourths,

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and we could rewrite that if we like.

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Both six and four are divisible by two,

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so let be divide both the[br]numerator and the denominator

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by two and we get three[br]halves, and we're done.