Here is how to find the slope. We saw in the lesson about what is slope that slope is a measure of how steep a line is

That steepness can be measured with the following formula:

slope = 1/2 after simplification

what is the meaning of 1/2 ?

Since 1/2 is positive, you are going uphill. Now, suppose the unit is yard

1 is the rise. 2 is the run. This means that everytime you go up 1 yard, you go accross or horizontally 2 yards

This situation is not very steep. However, take a look at the following:

So, slope = 8/2 = 4 meters

4 meters = 4/1 meters. This means that each time you go 4 meters straight up, you only go 1 meter horizontally

This situation is very steep because you go up a lot compared to going horizontally

Now, let's see how to find the slope when we don't know the rise and the run.

If we graph the slope on the coordinate system, we will be able to derive another useful formula

Let us then try to put a slope of 8 as in previous example on the coordinate system.

Put a rise of 8 anywhere you wish. Then, put a run of 2. Here we go!

. Then, label the two endpoints with their respective coordinates

Notice that 9 − 1 = 8. But 9 and 1 represent y-coordinates

Since we cannot call both coordinates y, we can call one y

Let y

Let y

Therefore, 9 − 1 = y

Notice also by the same token that 4 − 2 = 2. But 4 and 2 represent x-coordinates

Since we cannot call both coordinates x, we can call one x

Let x

Let x

Therefore, 4 − 2 = x

We can see then that

y

x

The formula becomes:

1) (8, 8) and (4, 4)

Let (x

(y

2) (1, -5) and (2, -10)

Let (x

(y

Notice that

(y

In general slope = (y

Now don't you wonder anymore about how to find the slope!