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.