This video explains how to find the equation of a line, given a point and the slope of the line. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.

There are two ways of solving this.

One way is using the slope-intercept formula, y = mx + b

And the other way is by using the point-slope formula, $y - y_1 = m(x - x_1)$

Example of Finding The Equation Of A Line, Given The Slope And A Point

Example 1

Find the equation of the line that passes through the point $( -2 , 6 )$ with a slope of $3$.

Let’s solve this using the point-slope formula which is

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

Now, let’s substitute

$y - (6) = 3 (x - (-2))$
$y - (6) = 3 (x +2)$

Now, let’s manipulate this to get the slope-intercept form

$y - 6 = 3x + 6$

Now, let’s isolate $y$ by adding $6$ on both sides.

$y - 6 +6 = 3x + 6+3$
$y = 3x + 12$

Example of 2

Find the equation of the line that passes through the point $( -5 , 2 )$ with a slope of $\dfrac{-3}{4}$.

Let’s solve this is using the slope intercept form directly.

$y = mx + b$
$y = \dfrac{-3}{4}x + b$

Multipy $4$ on both sides

$4y = -3x + 4$

Let’s solve for $b$ by substituting the values of $x$ and $y$.

$4(2) = \dfrac{-3}{-5} + 4b$
$8 = 15 + 4b$

Then isolate $b$ by subtracting $15$ on both sides

$8-15= 15 + 4b-15$
$-7 = 4b$

Divide $4$ to isolate $b$

$\dfrac{-7}{4} = \dfrac{4b}{4}$
$\dfrac{-7}{4} = b$

Now let’s write our slope intercept form
$y = \dfrac{-3}{4}x - \dfrac{7}{4}$

Video-Lesson Transcript

Let’s go over finding the equation of a line, given a point and the slope.

We’re going to use the slope intercept formula:

$y = mx + b$

For example:

$(2, 5)$, $m = -2$

We’re going to solve this in two different ways.

First is the point-slope formula which is

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

Now, let’s substitute

$y - 5 = -2 (x - 2)$

Now, let’s manipulate this to get the slope intercept form

$y - 5 = -2x + 4$

Now, let’s isolate $y$ by adding $5$ on both sides.

$y - 5 + 5 = -2x + 4 + 5$
$y = -2x + 9$

Or the second way to solve this is to do the slope intercept form directly.

$y = mx + b$
$y = -2x + b$

Let’s solve for $b$ by substituting the values of $x$ and $y$.

$5 = -2(2) + b$
$5 = -4 + b$

Then isolate $b$ by adding $4$ on both sides

$5 + 4 = -4 + 4 + b$
$9 = b$

Now let’s write our slope intercept form

$y = -2x + 9$

which is the same as our first answer.