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

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.

Finding the Equation of a Line