Writing Equations Using Point-Slope Form

Are you looking for an easy method to write linear equations when given slope and a point?

Point-Slope Form is the answer!

You've found the right page! Yes, Algebra teachers do try to make it easier for you to write these equations. There is yet another form that can be used to write linear equations in slope intercept form.

This form is particularly useful when writing equations give slope and a point, but can also easily be used to write equations given two points.

So, What is Point-Slope Form?

Point-slope form is y - y1 = m(x - x1), where (x1 and y1) are the coordinates of a point on the line, and m is the slope of the line. Take a look....


Point Slope Formula


How Do You Use Point-Slope Form?

So, this form looks a little complicated, how is it used? It's really pretty easy. It just takes a little substitution and rewriting the equation in slope intercept form.

Let's take a look at an easy problem given slope and a point.



Example 1: Using Point-Slope Form

Write the equation for a line that has a slope of 3 and passes through the point (2,1).

Solution

Using point-slope form to write an equation.


That wasn't too bad, was it? I think this is a pretty easy form to use once you use it a few times.

We will have to add one additional step to this process if we are given a problem with two points.

You will always need to know the slope in order to use this equation. But, that's not a problem when you know the formula for finding slope given two points.

So, take a look with me.....



Example 2: Writing Equations Using Point-Slope Form

Write an equation for a line that passes through the following points: (-4,4) and (6,9)

Solution

Using Point-slope form
point-slope continued


As you can see, point-slope form is pretty easy to use once you learn how to substitute for the slope and one point. Just remember: You must know (or be able to find) the slope and you must also know one point that lies on the line.

If you are still having difficulty, take a look at the following video, which will walk you step by step through example 2 above.




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