# How to Find the Slope of a Line Given the Two Coordinates of its Points

## Where to Begin

First, let us define what the slope of a line is. The slope of a line is the change in y divided by the change in x or rise over run. You can also think of slope as the "steepness" of the line. Finding the slope of a line is simple if you're given the coordinates of any two points. Let's start with an example:

Let's say we have two points (X1,Y1), (X2,Y2) such that, X1= 1, Y1 = 4 X2 = 3 and Y2 = 8. Next, we simply apply the equation for the slope of a line which is

m = Y2-Y1 ⁄ X2-X1.

Then we plug in the values for X2, X1,Y1, and Y2, and we obtain the following:

m = (8-4) ⁄ (3-1) = 4 ⁄ 2 = 2. Therefore the slope of this line is 2.

Here are some things to remember:

1) When you are given two pairs of coordinates (X2,Y2) and (X1,Y1), it does not matter which numbers replace which coordinates as long as you are consistent. For example, if we take the example above, I could have written Y2=4, Y1=8, X2=1 and X1=3. The resulting equation would look like this:

m = (4-8) ⁄ (1-3) = -4 ⁄ -2 = 2.

Notice that the slope is the same as before.

2) If X2 = X1, the denominator evaluates to 0. Therefore, the line will always be vertical because the X coordinate is always the same. Also, a vertical line is said to have no slope because division by zero is undefined.

For example,

m = (17-5) ⁄ ( 5 - 5) = 12 ⁄ 0 = undefined slope.

3) If Y2 = Y1, that means the slope = 0.That does not mean that your line has no slope; It simply means that your graph contains the slope of a horizontal line where all points along the Y coordinate are the same.

For example,

m = (13-13) ⁄ (4-2) = 0 ⁄ 2 = 0.

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