This video explains how to find the equation of a line when given 2 points.

Find the slope using the slope formula, .

After finding the slope, plug in the value of your points into either slope-intercept form, or point-slope form, to get the equation of the line. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

Examples of Finding The Equation Of A Line, Given Two Points

### Example 1

Find the equation of the line passing through the points and .

First, let’s find the slope.

Let’s label the given:

Next, let’s find the y-intrecept by using slope intercept form.

Substitute any of the paired coordinates but not both.

Let’s solve for

Now, we know what the y-intercept is and the slope.

So the equation becomes

### Example 2

Find the equation of the line passing through the points and

First, let’s find the slope.

Let’s label the given:

Next, let’s solve using point slope form.

Now, let’s get by itself by adding on both sides.

The answer will be:

## Video-Lesson Transcript

Let’s find an equation of a line, given two points.

How do we do this?

We can solve this by using the slope intercept form:

or by using point-slope formula:

But in both cases we need to know what the slope (m) is.

So the first step is to find the slope.

The formula for finding the slope is

For example:

Find the equation of a line with given points and

First, let’s find the slope.

Let’s label the given:

So now, we can find the equation of a line using the slope intercept form or the point slope form.

Let’s do the slope intercept form first.

Now, you can substitute any of the paired coordinates but not both.

I’m going to use the second pair of coordinates ,

Now, let’s solve for

Now, we know what the y-intercept is and the slope.

So the equation becomes

Now, let’s solve using the point-slope form.

Here, we can choose which pair to use as coordinates.

So let me choose the first set of coordinates ,

Also, we already know what the slope is

Now, let’s solve

Let’s get by itself by adding on both sides.

And our answer is

which is the same as the first one.