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# Point Slope Form Calculator

To find point slope form/equation of line (y-y_{1}=m(x-x_{1})) use our Point slope form calculator.

## Point slope form calculator

Point slope form calculator is an online tool to find the general equation of a line as ** Ax + By + C = 0. **All it needs is a slope

**and coordinates of point**

*m***in the two-dimensional Cartesian coordinate plane. Point slope calculator is an intuitive tool that lets you calculate the slope of line in no time.**

*A (x*_{1}, y_{1})## What is the point slope form?

The point slope form is defined that the difference in the y coordinate between two points (y - y_{1}) on a line that is proportional to the difference in the x coordinate points (x - x_{1}). The point-slope form is about having a single point and a direction and converting that between an algebraic equation and a graph.

It can also be stated as:

**“**The equation of a straight line in the form ** y − y_{1} = m(x − x_{1})** where m is the slope of the line and

**are the coordinates of a given point on the line.**

*(x*_{1}, y_{1})**”**

**Point slope formula**

The point slope formula can be expressed as:

**y - y _{1} = m(x- x_{1})**

Where:

refers to the slope of line,*m*represents the coordinate on x-axis, and*x*represents the coordinate on y-axis.*y*

The point-slope form is about having a single point and a direction and converting that between an algebraic equation and a graph. We can derive the slope of a line formula from the above point slope form equation.

**m = (y - y _{1}) / (x- x_{1})**

## How to find point slope form?

The point slope form can be calculated using the above point slope formula calculator. On the other hand, it can also be calculated using the formula for point slope form stated above. To find the point slope form manually, follow the steps below:

- Write down the coordinates for
,*x*_{1}and slope*y*_{1,} - Write down the point slope formula.
- Substitute the values in the formula and calculate the equation of line.

## Point slope equation calculator Examples:

**Example 1:**

Find the equation of the line that passes through ** (-3, 1)** with a slope of

*2.***Solution:**

** Step 1:** Write down the coordinates for

**,**

*x*_{1}**and slope**

*y*_{1,}

*m.**x _{1}* = -3,

*y*= 1, and

_{1}slope

*m*= 2

** Step 2:** Write down the point slope formula and apply that formula.

y - y_{1} = m(x- x_{1})

** Step 3:** Substitute the values in the formula and calculate the equation of line.

y - 1 =2(x - (-3))

y - 1 = 2(x + 3)

y - 1 = 2x + 6

Therefore the Equation = 2x + 6 – y + 1

Equation of the line = 2x – y + 7

**Example 2**

How do you find the point slope form of point (2, 5) and slope -3?

**Solution**

** Step 1:** Write down the coordinates for

**,**

*x*_{1}**and slope**

*y*_{1,}

*m.**x _{1}* = 2,

*y*= 5, and

_{1}slope

*m*= -3

** Step 2:** Write down the point slope formula and apply that formula.

y - y_{1} = m(x- x_{1})

** Step 3:** Substitute the values in the formula and calculate the equation of line.

y - 5 =-3(x - (2))

y - 5 = -3(x - 2)

y - 5 = -3x + 6

= 3x + y – 5 + 6

Equation of the line = -3x - y + 11

**Example 3:**

Find the equation of the line that passes through (-3, 1) with a slope of 2.

x_{1} = -3,

y_{1 }= 1 and

slope m = 2.

__Apply Formula__:

y - y_{1} = m(x- x_{1})

y-1 =2(x-(-3))

y-1 = 2(x+3)

y-1 = 2x+6

Therefore the Equation = 2x+6-y+1

**Equation of the line = 2x-y+7**

**References: **

- Definition of POINT-SLOPE FORM Merriam-webster.com.
- Stapel, E. (2020). Straight-Line Equations: Point-Slope Form | Purplemath.
- Point-Slope Equation of a Line. Mathsisfun.com.
- Point Slope Form of a Line, examples, graphs, and video tutorials Mathwarehouse.com
- Point Slope Form (Simply Explained with Examples!)Calcworkshop.
- Estela, M. (2020). Point-Slope Form of a Straight Line with Examples | ChiliMath.