Point slope form calculator

The formula of point-slope form calculator is used to find the equation of a Straight line.

Point Slope Form Calculator
NOTE :-If your slope is fraction, please convert in to decimal, then enter the slope in the box provided.
Example : 1/2 to be entered as 0.5

There are some other different forms of the equation of a straight line.

  • Point Slope Form
  • Slope Intercept Form
  • Intercept form
  • Two points form.

What is Point Slope Form?

This formula is used only when we know the slope of the straight line and a point on the straight line.

The equation of a straight line whose slope is m and which passes through a point (x1, y1) is found using the point slope form.

Point-Slope Form

The equation of the point-slope formula is:

y – y1 = m ( x – x1)

Point-Slope Form equation of the line

Point Slope form Calculator

The equation for the slope of a straight line is:

y – y1 = m ( x – x1)
Equation DescriptionDerivation method
The equation for the slope of a straight line isSlope\;m=\frac{Diff.\;in\;y\;-\;coordinate}{Diff.\;in\;x\;-\;coordinate}
Now the Equation is :m=\frac{y\;-\;y1\;}{x-\;x1}
Multiplying both sides by (x−x1)m\;(x\;-\;x1)\;=\;y-\;y1
This can be written as,y-\;y1\;=\;\;m\;(x\;-\;x1)

where,

  • (x, y) is a random point on the straight line used as variables while applying the formula.
  • (x1,y1) is a fixed point on the straight line.
  • m is the slope of the straight line.

The equation is useful only when we have:

  • one point on the line: (x1,y1)
  • and the Slope of the line: m,

Hence the point-slope formula is proved.

Slope-Intercept Form

slope-intercept form

Slope-intercept form calculator is the commonly used form for the equation of a line and is derived as,

y = mx + b
Equation DescriptionDerivation method
The Point-Slope Form equation isy-\;y1\;=\;\;m\;(x\;-\;x1)
(x1 , y1) is actually (0 , b)y\;-\;b\;=\;m\;(x\;-\;0)
That is y\;-\;b\;=\;m\;x
Put b on another sidey\;=\;m\;x\;+\;b

where,

  • b is the value called the y-intercept.
  • m is the slope.
  • point (x1, y1) is actually at (0, b).

It is same as point-slope form except that this equation involves the slope of a line and its y-intercept point, rather than the slope of a line and a point on the line.

It is the advance case of point-slope form shows that the point on the line is also the y-intercept.

Because of the slope and y-intercept, it is easy to write the equation of a line in slope-intercept form, and also to graph it.

Hence the slope-Intercept form is proved.

Intercept Form

Intercept Form

Intercept form equation of a line is one of the method to find the equation of a line.

Here, we will find the equation of a straight line by using x- intercept and y - intercept. 

The Intercept Form is expressed as,

\frac{x}{a}+\frac{y}{b}=1
Equation DescriptionDerivation method
The Intercept Form equation is\frac{x}{a}+\frac{y}{b}=1

Where,

  • x- intercept  =  a
  • y- intercept  =  b

Solved Examples

Example 1 :

Question : - (x1, y1) = (3, 6) And m = 7

Answer :-

DescriptionSolved Equation
The slope of the line l isy - y1 = m (x - x1)
Put values as mentioned in the question.
Now the equation will be :
y - 6 = 7 (x - 3)
Now multiply 3 by x-2y - 6 = 7x - 21
Which can be specified as:y=7x-21+6
y=7x-15
Final Equation7x-y-15=0

Example 2 :

Question : - (x1, y1) = (2, 4) And m = 6

Answer :-

DescriptionSolved Equation
The slope of the line l isy - y1 = m (x - x1)
Put values as mentioned in the question.
Now the equation will be :
y - 4 = 5 (x - 2)
Now multiply 2 by x - 1y - 4 = 5x - 12
Which can be specified as:y=5x -10 + 4
y = 5x - 6
Final Equation5x-y-6=0

Frequently Asked Questions

What is the point slope form equation ?

The equation is y-y₁=m(x-x₁) for linear equations.

How to calculate point slope equation online ?

You can calculate the point-slope equation online by point slope calculator

What is the Slope-Intercept form equation ?

The linear equation of slope-intercept form is y = mx + b.

How to calculate slope intercept online ?

You can calculate the slope-intercept equation online by slope intercept calculator