equation of the straight line

Point slope form calculator

Looking for online point slope form calculator to find the equation of the line ? If yes then this calculator is for you.

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

Point Slope Form Calculator is a free online tool that shows the equation of a line using the value x1,y1 and line's slope m.online point-slope form calculator tool makes the calculation easier, and it displays the form in a fraction of seconds.

How to use Point Slope Form Calculator ?

The procedure to use the point-slope form calculator is as below:

  • Step 1: Enter the values of X1,Y1 & M slope in the value box.
  • Step 2: Click on Calculate button in the middle of the calculator.
  • Step 3: Check below value box for the equation of the line.

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

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What are the formulas for slope?

There are three equations of linear.

  • Point slope form.
  • Slope intercept form.
  • Standard form

For easy,you can use our free online point slope formula calculator for the point-slope calculations.

What is Point Slope Form?

This form is particularly get use when information is provided of single point sf the line and slope of a line.

These two pieces of information are enough to complete the linear equation and if we indeed given up the point and slope then is only feeding that we use point slope , the most easy form to get to find the linear equation.

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.

So,let us present you the equation of the point-slope formula:

y – y1 = m ( x – x1)

What is an Equation of the line

Point-slope-form-graph

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.
  • m is the slope of the straight line.
  • (x1,y1) is a fixed point on 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.

What is 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,

  • m is the slope.
  • b is the value called the y-intercept.
  • 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 , 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.

What is Intercept Form

Intercept Form

The 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

How to solve point slope form (step-by-step) manually ?

All right,lets go through the example step by step.

Example 1 :

Question : - What is the point slope equation of a line that is having a slope m= 5 & goes through the point (x1, y1) = (2, 1) ?

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 - 1 = 5 (x - 2)
Now multiply 5 by x-2(y-1)=5(x-2)
Which can be specified as:y=5x-10+1
y=5x-9
Final Equation5x-y-9=0

Example 2 :

Question : - What is the point slope equation of a line that is having a slope m= 6 & goes through the point (x1, y1) = (2, 4) ?

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 5 by x - 2y - 4 = 5x - 12
Which can be specified as:y=5x -10 + 4
y = 5x - 6
Final Equation5x-y-6=0

Solved Examples :



Frequently Asked Questions

How to calculate point slope equation online ?

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

How to calculate slope intercept online ?

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

What is the Slope-Intercept form equation ?

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

What is the point slope form equation ?

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

Conclusion

This point slope formula calculator is easy to use for the students who want to find the equation of the line quickly.