How to find the equation of a line with one point without slope

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,

Example 1

Find the equation of the line that passes through the point with a slope of .

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

Now, let’s substitute

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

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

Example of 2

Find the equation of the line that passes through the point with a slope of .

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

Multipy on both sides

Let’s solve for by substituting the values of and .

Then isolate by subtracting on both sides

Divide to isolate

Now let’s write our slope intercept form

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:

For example:

,

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

First is the point-slope formula which is

Now, let’s substitute

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

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

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

Let’s solve for by substituting the values of and .

Then isolate by adding on both sides

Now let’s write our slope intercept form

which is the same as our first answer.

How do you find the equation of a line with one point?

What is the equation of a line with no slope?

How do you find slope with 1 point?