About this video
The video finds the slope of a line from a table of points using slope = change in y / change in x, or (y2 - y1) / (x2 - x1). In the first table, going from (2, 4) to (3, 1) gives a slope of -3/1 = -3. In the second, going from (1, 7) to (5, 13) gives 6/4 = 3/2.
You'll be able to
- state that slope is change in y divided by change in x.
- calculate slope from any two points in a table.
- keep track of signs when a value decreases, and simplify the slope fraction.
Key words
- slope
- How steep a line is: the change in y divided by the change in x between two points.
- delta
- The Greek letter that looks like a triangle; it is shorthand for 'change in'.
- starting point and ending point
- The two points (x1, y1) and (x2, y2) you use to measure the changes in x and y.
Transcript
- [Instructor] 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. Alright, 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, look likes 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 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?
So we're going from two to three, so our change in x 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 y? Our change in y is our finishing y one minus our starting y four, which is equal to negative three.
And you could of, you didn't even have to do this math, 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 y over change in x?
Well, it's going to be, our change in y is negative three and our change in x is one. So our slope is negative three divided by one 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 pause the video again and see if you can figure it out.
Alright, 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 13, 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 case it's a positive. When x increases, y increased as well. So 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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