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

Find the slope using the slope formula, $m = \dfrac{y_2 - y_1}{x_2 - x_1}$.
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 $(-5, 7)$ and $(2, 3)$.

First, let’s find the slope.

Let’s label the given:

$x_1 = -5$, $y_1 = 7$
$x_2 = 2$, $y_2 = 3$
$m = \dfrac{y_2 - y_1}{x_2 - x_1}$
$m = \dfrac{3 - 7}{2 - (-5)}$
$m = \dfrac{-4}{7}$

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

$y = mx + b$
$y = \dfrac{-4}{7}x + b$
$7y=-4x+7b$

Substitute any of the paired coordinates but not both.

$x_1 = -5$, $y_1 = 7$
$7(7) = \dfrac{-7} {-5}+ 7b$

Let’s solve for $b$

$49 = 20 + 7b$
$49- 20 = 20 +7b-20$
$29 = 7b$
$\dfrac{29}{7} = \dfrac{7b}{7}$
$\dfrac{29}{7} = b$

Now, we know what the y-intercept is and the slope.
So the equation $y = mx + b$ becomes

$y = \dfrac{-4}{7}x + \dfrac{29}{7}$

### Example 2

Find the equation of the line passing through the points $(-4, 2)$ and $(1, -6)$

First, let’s find the slope.

Let’s label the given:

$x_1 = -4$, $y_1 = 2$
$x_2 = 1$, $y_2 = -6$
$m = \dfrac{y_2 - y_1}{x_2 - x_1}$
$m = \dfrac{-6 - 2}{1- (-4)}$
$m = \dfrac{-8}{5}$

Next, let’s solve using point slope form.

$y - y_1 = m (x - x_1)$
$y - 2 = \dfrac{-8}{5} (x - (-4))$
$y - 2 = \dfrac{-8}{5} (x +4)$
$y - 2 = \dfrac{-8}{5}x -\dfrac{8}{5}(4)$
$y - 2 = \dfrac{-8}{5}x -\dfrac{32}{5}$

Now, let’s get $y$ by itself by adding $2$ on both sides.

$y - 2 +2 = \dfrac{-8}{5}x -\dfrac{32}{5}+2$

$y = \dfrac{-8}{5}x -\dfrac{22}{5}$

## 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:

$y = mx + b$

or by using point-slope formula:

$y - y_1 = m (x - x_1)$

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

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

For example:

Find the equation of a line with given points $2, 4$ and $4, 5$

First, let’s find the slope.

Let’s label the given:

$x_1 = 2$, $y_1 = 4$
$x_2 = 4$, $y_2 = 5$
$m = \dfrac{y_2 - y_1}{x_2 - x_1}$
$m = \dfrac{5 - 4}{4 - 2}$
$m = \dfrac{1}{2}$

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.

$y = mx + b$
$y = \dfrac{1}{2}x + b$

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

I’m going to use the second pair of coordinates $x_2 = 4$, $y_2 = 5$

$5 = \dfrac{1}{2} (4) + b$

Now, let’s solve for $b$

$5 = 2 + b$
$5 - 2 = 2 - 2 + b$
$3 = b$

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

So the equation $y = mx + b$ becomes

$y = \dfrac{1}{2}x + 3$

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

$y - y_1 = m (x - x_1)$

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

So let me choose the first set of coordinates $x_1 = 2$, $y_1 = 4$

Also, we already know what the slope is $m = \dfrac{1}{2}$

Now, let’s solve

$y - 4 = \dfrac{1}{2} (x - 2)$
$y - 4 = \dfrac{1}{2}x - 1$

Let’s get $y$ by itself by adding $4$ on both sides.

$y - 4 + 4 = \dfrac{1}{2}x - 1 + 4$

$y = \dfrac{1}{2}x + 3$