When you’re trying to find the slope between two points on a graph, the coordinates are really important.

The slope can be calculated using this formula:

$$\text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1}$$

In this formula, $(x_1, y_1)$ and $(x_2, y_2)$ are the two points you’re looking at.

What are Coordinates?

Let’s say we have two points:

• Point A: $A(2, 3)$
• Point B: $B(5, 7)$

In Point A, $x_1 = 2$ and $y_1 = 3$.

For Point B, $x_2 = 5$ and $y_2 = 7$.

How to Find the Slope

To find the slope, we can plug the coordinates into our formula:

$$m = \frac{7 - 3}{5 - 2} = \frac{4}{3}$$

This means that the slope between points A and B is $\frac{4}{3}$.

What this tells us is that for every 4 units you go up, you move 3 units to the right.

What Happens With Different Points?

Now, let’s look at what happens if the points change.

For example, we have:

• Point C: $C(2, 1)$
• Point D: $D(5, 2)$

Let’s find the new slope:

Using the same formula:

$$m = \frac{2 - 1}{5 - 2} = \frac{1}{3}$$

This time, the slope is $\frac{1}{3}$.

This slope is less steep compared to the first example.

In Summary

In summary, the slope formula stays the same, but different coordinates change how steep the slope is and which way it goes.

That’s why knowing how to calculate the slope is key for solving problems and for drawing straight lines on a graph!