Point slope form calculator with steps

Point slope form calculator is an online tool used to find the linear equation of the line by using the coordinate points (x1, y1) and the slope of the line.

There are various methods to find the equation of the straight line such as point-slope form, slope-intercept form, and two-point intercept form. 

What is point-slope form?

The point-slope form is a technique used to find the straight-line equation. The point-slope form follows an equation:

(y – y1) = m(x – x1)

• x & y are the fixed points of the line.
• (x1, y1) are the coordinate points of the line.
• & m is the slope of the line

How to find the point-slope form?

Below are a few solved examples of the point-slope form.

For positive coordinate points

Example

Find the linear equation of the line if the slope is 4 and the coordinate points are (3, 5).

Solution 

Step 1: Identify the given values.

x1 = 3
y1 = 5
slope = m = 4

Step 2: Take the formula of the point-slope form and substitute the given values.

(y – y1) = m(x – x1)
(y – 5) = 4(x – 3)
y – 5 = 4x – 12 
y – 5 – 4x + 12 = 0
y – 4x + 7 = 0 

Multiply by -1 on both sides of the above expression.

-1(y – 4x + 7) = -1(0) 
-y + 4x – 7 = 0 
4x – y – 7 = 0 

For negative coordinate points

Example

Find the linear equation of the line if the slope is 3.5 and the coordinate points are (-13, -12).

Solution 

Step 1: Identify the given values.

x1 = -13
y1 = -12
slope = m = 3.5

Step 2: Take the formula of the point-slope form and substitute the given values.

(y – y1) = m(x – x1)
(y – (-12)) = 3.5(x – (-13))
(y + 12) = 3.5(x + 13)
y + 12 = 3.5x + 45.5 
y + 12 – 3.5x – 45.5 = 0
y – 3.5x – 33.5 = 0 

Multiply by -1 on both sides of the above expression.

-1(y – 3.5x – 33.5) = -1(0) 
-y + 3.5x + 33.5 = 0 
3.5x – y + 33.5 = 0 

Try the point slope form calculator to cross-check the above result.