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Slope

Learn how to calculate slope from a graph and from a pair of coordinates. Learn about the different types of slope- positive slope, negative slope, zero slope (no slope), and undefined slope.

Slope=m=\frac{y_2 - y_1}{x_2 - x_1}

Video-Lesson Transcript

In this lesson you’ll learn all about slopes.

A slope tells us how steep a line is. And how quickly it goes up or how quickly it goes down.

We can simply put it as slope = \dfrac{rise}{run}.

Whereas rise is how high it goes up and run is how far it is from the origin.

Here we have a point with (2, 3) coordinates and the origin has (0, 0) coordinates.

We can count how high the slope is using the graph.

Here we have rise = 3 and run = 2

So our slope is = \dfrac{3}{2}.

But we can also determine the slope without using the graph.

Let’s use this formula:

Slope = m = \dfrac{y_1 - y_2}{x_1 - x_2}

This makes sense because the change in y-coordinates will tell us how high it goes and the change in x-coordinates will tell us how far over it runs.x runs horizontally and y is vertically.

So, let’s go back to our example of a point with (2, 3) coordinates and the origin has (0, 0) coordinates.

Let’s use the formula and substitute the given

Slope = m = \dfrac{y_1 - y_2}{x_1 - x_2} Slope = m = \dfrac{3 - 0}{2 - 0} m = \dfrac{3}{2}

Again, we got the same answer. Either we use the graph or the formula.

Different Types of Slope

Now let’s take a look at different types of slopes.

The first slope we see goes from left to right upwards.

This is called a positive slope m = +. Or we could also say that the slope is greater than 0 m > 0.

The second slope we have goes from left to right downwards.

This is called a negative slope m = (-). Or we could say that the slope is less than 0 m \textless 0.

The third slope is a straight horizontal line. This is a strange slope.

Remember the formula for slope?

m = \dfrac{y_1 - y_2}{x_1 - x_2}

When we pick any two points, there’s one and the same y-coordinate. So if we subtract the numerator, our answer is 0. So the slope is also 0. Remember that0 divided by any number is 0.

Thus, we call this zero slope.

The last slope we have is straight vertically. If the third slope is strange, this one is even more peculiar.

Using the same logic as the third slope, let’s pick any two points. Here, our x-coordinate is the same since it’s vertically straight line. Using the formula, our denominator is 0.

Very important to note that

\dfrac{4}{0} \neq 0

Remember, any number divided by 0 does not exist.

Thus, we call this an undefined slope.

So just to recap, there are four types of slopes.

Positive slope when the line from left to right goes upwards.

Negative slope when the line from left to right goes downward.

Zero slope when the line is straight horizontally.

And an undefined slope when the line is straight vertically.