X

Point Slope Form Calculator

Point Slope Form Calculator

Is This Tool Helpful?

     

Formula

Point slope form = y - y1 = m(x- x1)

The point slope form is defined that the difference in the y coordinate between two points (y - y1) on a line is proportional to the difference in the x coordinate points (x - x1). Enter values in point slope form calculator below to find the Equation of a straight line.Point-slope form is about having a single point and a direction and converting that between an algebraic equation and a graph.

Point slope form calculator is an online tool to find the general equation of line as Ax + By + C = 0. All it needs is a slope m and coordinates of a point A (x1, y1) 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.

Keep reading if you want to know how to use this calculator, point slope form definition, point slope form equation, how to calculate equation of line, and much more.

How to use point slope form calculator?

The point slope equation calculator comes with a simple interface which makes it more user friendly. This tool is not limited to the students. Anyone can use it including teachers, engineers, computer graphics experts, aeronautical staff, etc. To use this tool, follow the below steps:

  • Enter the coordinate for X1 in the given input box.
  • Enter the coordinate for Y1 in the next input box.
  • Enter the coefficient of slope m in the respective input box.
  • Hit the Calculate button after entering all values.
  • Use the Reset button to enter new values.

You will get the equation of straight line very smoothly after filling the required fields. Not only equation of line, it also draws the line on a Cartesian plane for further clarification.

Point slope form and point slope intercept form both fulfil the same purpose of drawing a straight line equation. If you want to find out equation of line using slope intercept, you can use our slope intercept form calculator anytime.

What is point slope form?

Point Slop Diagram

The point slope form is defined as the difference in the y coordinate between two points (y - y1) on a line is proportional to the difference in the x coordinate points (x - x1).

It can also be stated as:  

The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line.Merriam-Webster.

Point slope formula

The point slope formula can be expressed as:

Point slope form = y - y1 = m(x- x1)

Where:

m refers to the slope of line,

x represents the coordinate on x-axis, and

y represents the coordinate on y-axis.  

Point Slop Form      

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 - y1) / (x- x1)

How to find point slope form?

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 x1, y1 and slope
  • Write down the point slope formula.
  • Substitute the values in the formula and calculate the equation of line.

Point slope equation calculator Examples:

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

Solution:

Step 1: Write down the coordinates for x1, y1 and slope m.

x1 = -3,
y1 = 1, and
slope m = 2

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

y - y1 = m(x- x1)

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

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

Step 1: Write down the coordinates for x1, y1 and slope m.

x1 = 2,
y1 = 5, and
slope m = -3

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

y - y1 = m(x- x1)

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 - point-slope form

Find the equation of the line that passes through (-3, 1) with slope of 2.
x1 = -3,
y1 = 1 and
slope m = 2.

Apply Formula:
y - y1 = m(x- x1)
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