Point Slope Form Calculator 2023

Hello Students, Are you looking for a Point slope form calculator with two points to find the equation of the line? If yes then this tool is for you.

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

According to Wikipedia, a linear equation is an equation that may be put in the form of coefficients which are often real numbers. Also, the Slope Intercept Form Calculator is available for free.

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


How to use Point Slope Form Calculator?

The procedure to use the point-slope formula tool 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 the below value box for the equation of the line.

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


What is Point Slope Formula?

What is Point Slope Form?
What is Point Slope Formula?

This form is particularly getting used when information is provided about a single point of the line and the slope of a line.

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

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

The point-slope form is useful because it allows you to find the equation of a line given just a point on the line and the slope of the line, rather than having to find two points on the line and use them to calculate the slope and y-intercept.

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

y - y1 = m ( x - x1 )


What is an Equation of the line

What-is-an-Equation-of-the-line
What-is-an-Equation-of-the-line

An equation for the slope of the straight line is :

Slope\;m=\frac{Diff.\;in\;y\;-\;coordinate}{Diff.\;in\;x\;-\;coordinate}

After that simplification will be :

m=\frac{y\;-\;y1\;}{x-\;x1}

Multiplying both sides by (x−x1) :

m\;(x\;-\;x1)\;=\;y-\;y1

The equation for the slope of a straight line can be written as :

y-\;y1\;=\;\;m\;(x\;-\;x1)

where,

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

the equation is useful only when we have:

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

Therefore, the point-slope formula is proved.

It's also important to note that the point-slope form is a way to represent a linear equation, as long as you know one point that the line goes through, and the slope of the line, you can use this form.

In other words, this form of the equation is useful when we have a slope and one point, and we want to find the equation of a line.


What is Slope-Intercept Form

What-is-Slope-Intercept-Form
What-is-Slope-Intercept-Form

Slope-intercept form calculator is the commonly used form for the equation of a line.

The Point-Slope Form equation is :

y - y1 = m (x - x1)

(x1, y1) is actually (0, b) :

y - b = m (x - 0)

So it simplifies as :

y - b = mx

Put b on another side :

y = mx + b

where

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

It is the same 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 advanced case of a point-slope form calculator with two points that show 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 in slope-intercept form, and also to graph it.

Therefore, the slope-Intercept form is proved.


What is Intercept Form

Whati-is-Intercept-Form
What-is-Intercept-Form

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

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

The Intercept Form is expressed as,

\frac{x}{a}+\frac{y}{b}=1

Where,

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

How to find the equation of the line with coordinates and slope of a point?

All right, let's go through the example step by step.

Example 1 :

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

Answer:- Let's have a look at the values given in the question.

Step 1: Substitute the given values of m & (x1,y1) into the point-slope form.

y - 1 = 5(x - 2)

Step 2: Simplify the equation by distributing the 5 on the right side of the equation.

y - 1 = 5x - 10

Step 3: Add 1 to both sides of the equation to get y by itself.

y = 5x - 9

So the point-slope equation that is having a slope m= 5 & goes through the point

(x1, y1) = (2, 1) is y = 5x - 9.

Step 4: Write down the answer in the form of an equation.

5x - y - 9 = 0


Example 2 :

Question: - What is the point-slope form calculator with two points of a line that is having a slope is 6 & goes through the point (x1, y1) = (2, 4)?

Answer:-

Step 1:Identify the slope of the line: m = 6

Step 2:Identify a point on the line: (x1, y1) = (2, 4)

Step 3: Substitute the values into the point-slope form of a line equation.

y - 4 = 6(x - 2)

Step 4: Simplify the equation.

y - 4 = 6x - 12

Step 5: Write the equation in slope-intercept form (y = mx + b).

y = 6x + (-12+4)

The final Answer is y=6x - 8


Solved Examples :



Frequently Asked Questions for point slope form calculator

How to calculate the point-slope equations 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

What is the point-slope form equation?

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


My Conclusion on point slope form calculator

The point-slope formula is a way to express an equation of a straight line in terms of a point on the line and the slope of the line. This point slope form calculator is easy to use for students who want to find the equation of the line quickly.


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