Point Slope Form (Simply Explained w/ 17 Examples!)

Just like there is more than one way to peel an onion, there are several ways to write the equation of a line.

Jenn (B.S., M.Ed.) of Calcworkshop® introducing point slope form

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

Ultimately, it comes down to preference, but in my humble opinion, there is one method that is far better than the rest: Point Slope Form!

The Point-Slope equation is specifically designed to handle the trickiest type of questions, namely, how do you write an equation given two points?

First, we take our two points and find the slope.
Next, we pick one of our two given points, and the slope we just found, and plug them into the point-slope form formula.
Done!

Remember, slope represents the steepness or the rate of change of our linear equation.

In fact, this method is so straightforward, that you will find writing linear equations super easy!

And through this lesson, we will discover that the point-slope form definition is really just an extension of our beloved slope formula.

Formula for Point Slope Form

It’s true! All we have to do is a little rearranging, as Math Is Fun so fittingly states, and we will see that point slope form is just the slope formula in disguise.

But the excitement continues…

… did you know that the point-slope form helps us approximate other points on a curve (i.e., linear approximation) and is also called a first-degree Taylor polynomial?

What?

Yep, this little formula is used in calculus to find the equation of a tangent line to a curve and helps us to represent a function as an infinite sum of terms.

And no matter where you are on your mathematical journey, the idea that Algebra and Calculus are intrinsically connected is just plain cool!

Here are a few examples just to give you a taste of what we will be doing in this lesson.

Seven Point-Slope Form Examples

How to find the y intercept given the slope and a point

Find the y-intercept with slope and point

Using point slope form to write the equation of a line in slope intercept form

Write an equation of a line given the y intercept and another point

Writing an equation in slope intercept form given two points

Using y-y1=m(x-x1) to write the equation of a line

Given the graph write the equation of the line

How to find y=mx+b with two points

Using the point slope formula to find the y intercept

Find the y intercept given two points

Use the alternate form of point slope form to write the equation of the line given two points

Use y=m(x-x1) + y1 to write the equation of the line

Write the equation of the line and then solve for y given a value of x

Given the Point (4,5) and Slope of 6, find y when x=24

So, together we are going to learn how to:

Write the equation of a line using point-slope form.
Represent equations from point slope form to slope intercept form.
Represent equations from point slope form to standard form.
Write equations of parallel lines and perpendicular lines by finding the line that passes through a point and has either parallel slope or perpendicular slope to the graph of a given equation.

Point Slope Form – Video

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