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

Find the slope using the slope formula,  m = \frac{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

The answer will be:

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

Finding the Equation of a Line 2

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

And our answer is

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

which is the same as the first one.