How To Convert Point Slope Form To Slope Intercept Form?


Yes, there is no doubt that mathematics is a tricky subject that is considered a combination of simple and complex domains. Every student has their own mindset and ability to understand various mathematical problems. But here we are going to eradicate this difficulty for you people. Yes, we are talking about nothing but a free online point slope form calculator. With the help of this free slope intercept form calculator, you can actually get to know how to find point slope form, and then how to convert this form to slope intercept form by using an online y intercept calculator.

So without getting further late, let us dive into it!

What is the point-slope form?

In geometric analysis:

“A particular form of the equation that lies on the line and is used to represent this line by using x and y coordinates of that point and the slope m is known as the point-slope form.”

General Form:

The generic form of the point-slope equation is given as below:

(y – y1) = m(x – x1)


(y – y1) = Difference among the y coordinates

(x – x1) = difference among the x coordinates

m = slope of the line on which these points lie

The free point slope form calculator also uses the same equation to swiftly determine the point slope form. 

Graph of Point Slope Form:


Find the point slope form of the equation having slope 5 and point as (2, 5)


Here we have:

(y – y1) = m(x – x1)

(y – 5) = 5(x – 2)

y – 5 = 5x – 10

y – 5 – 5x + 10 = 0

y – 5x + 5 = 0

Which is the required point slope form of the slope and points given. As you see that it is not a complicated calculation, but for those who still did not get it, use the free point slope calculator for free to generate accurate and immediate outputs.

Slope Intercept Form:

Below we have the general form of the slope intercept that could also be determined by using free slope intercept form calculator:

y = mx + c


m = Slope of the line 

x = Horizontal coordinate

y = Vertical coordinate

By putting the values in the above formula, you can write an equation in its slope intercept form. Also, the free write an equation in slope intercept form calculator also does the same for you but in a fragment of seconds.

Graph of Slope Intercept Form:

x – Intercept:

If you take y=0 in the equation of the slope intercept form, you will get x intercept as follows:

y = mx + c

0 = mx + c

mx = -c

x = -c/m 

y – Intercept:

When you put x=0 in the slope intercept equation, you will get y intercept :

y = mx + c

y = m(0) + c

y = 0 + c

y = c

This means that the y intercept is the point where the line touches the y axis. The same result can also be enumerated with the help of the free slope intercept form calculator.


What would be the x intercept for the slope intercept form equation below:

9y = 2x – 5


Here we have:

y = 0

Putting this value in the slope in the given equation:

9y = 2x – 5

9(0) = 2x – 5

2x – 5 = 0

2x = 5

x = 5/2

This is our required answer and can easily be determined by using the free slope intercept form calculator by

Conversion of Point Slope Form To Slope Intercept Form:

Well, here comes a little bit of technicality. But do not worry as both point slope form calculator and y intercept calculator would be eradicating these hurdles for you. Ok, let us move on!

  • What you need to do here is just to solve the point slope form equation for the variable y. 
  • When you apply inverse operations on all other variables and constants except y, you get the slope intercept form.


In this section, we will be resolving a couple of examples to clarify your idea in more depth. Just stay focused!

Problem # 01:

Convert the following point slope equation to slope intercept form:

6y + 3x + 2 = 0


The given equation is:

6y + 3x + 2 = 0

Solving for y:

6y + 3x = -2

6y = -2 – 3x

y = -2 – 3x / 6

y = -(3x + 2) / 6

Which is the resulting slope intercept form of the given equation. The interesting fact here is that the free slope and y intercept calculator does these calculations in seconds and saving your precious time for sure.

Problem # 02:

Determine the point slope form and then convert it to slope intercept form of the equation as under:

3x = 4y + 12


Here we have:

3x = 4y + 12

3x – 12 = 4y

(3/4)x – (12/4) = y


y + 3 = ¾ x

Which is the required point slope form which you can also find with the help of the free point slope form calculator.

Now converting to slope intercept form requires only one single step which is as follows:

y + 3 = ¾ x

y = ¾ x – 3

Which is our final outcome that can be instantly found with the help of a free slope intercept form calculator.

About Point Slope Form Calculator And Slope Intercept Form Calculator:

A special thanks to that has not designed both of these calculators for instant calculations, but also hundreds of such helping calculators. By using these two calculators that have been discussed in this article, anyone can get instant, accurate, and authentic results. Not only this, but you can also use other calculators to get a firm grip over the calculations and achieve good grades in the examination. Well, it may seem weird enough, but believe me, it really works.

Let’s Wind Up:

In this technical read, we discussed the point intercept and slope intercept forms separately. With that, their conversion has also been discussed properly by either manually or using free point slope form calculator and slope intercept form calculator. We hope this article will help you a lot in understanding the basics of the equation lines.

Good Luck!