Tilt

Slope

And as we go outside, our gradient becomes larger and larger.

What can I do?

It doesn't change the inclination of the line.

So that tells us, essentially, what the two asymptotes are.

But what is the slope of that tangent line?

It actually tilts.

I'm at an angle.

Whereas, the outer ones remain more or less fixed on the right it's the opposite.

It downloads right to the phone.

This has a y intercept also at 3, right there.

We could immediately say, OK, the y intercept is 2.

Derives a gradient of Y.

And here's the point of that.

Or you could say the difference in y over difference in x.

The first one was introduced by Hubble, and that's

So that should be the change in x, delta x.

So that is the slope of this secant

The line just barely touches it.

Those are the regression coefficients for this example.

So that's the same thing as y equals x plus one.

Because a line has the slope is consistent the whole way through it.

Positive values create a foward slant, negative values create a negative slant.

But we're not sloping we're not moving up as quickly as when we had y equals 2x. y equals 2x looked something like this.

It's decreasing by 4.

Now I've been showing you what happens to the slope.

And our y changed by 1

Where m is the slope.

And I'll switch colors just to ease the monotony.

You can just set this equal to 0 and it's equal to 6.

You really just have to know that it is tilted, and right now it is tilted at an angle of 23,4 .

Well we could just do that doing the algebra.

It is defined as the ratio of the time derivative of the scale factor by the scale factor itself.

Well, a couple of ways to think about it.

And just to get an intuition for what that means

So this is my y axis, this is my x axis, and I want to know the slope at the point x is equal to 3.

I've written down at the bottom there the slope of this curve, this straight line.

Notice y equals zero, x plus one.

And if you want a little review of algebra, this epsilon is actually going to be the slope of that line.

So this arrow and this arrow, they are both popping straight out of the North Pole.

What's the slope over here?

Let me pick a slightly thinner color, and we'll get started.

For every one that we go down, we go over two.

That is the age slope. Got steeper, negatively.