Overview of different forms of a line's equation
There are many different ways that you can express the equation of a line. There is the slope intercept form , standard form and also this page's topicpoint slope form. Each one expresses the equation of a line, and each one has its own pros and cons. Point Slope form, this page's topic, makes it easy to find the line's equation when you only know the slope and a single point on the line(see example 1).. Point slope form is also the quickest method for finding the equation of line given two points (see example 2).
Definition of the Point Slope Form Equation
The Point Slope Form Formula Example and Non Example EquationsExamples of Point Slope Form Equations  NonExamples 

y −5 = 3(x −2)  2y = 4x +2 
y + 5= ½(x − 12)  x = 6 − y 
y + 5= 4(x + 12)  y = 2x + 7 
y + ½= ¼(x + ¾)  3x + 5y = 2 
When is point slope form useful?
 When you do not know or need to know the intercepts (x and yintercepts) (Use Standard Form in this case)
 When you do know or can easily get the slope and 1 point.
When are other forms more useful?
 Standard Form is more convenient when you know or need to know the x intercept and also the yintercept and do not know the slope
 Slope intercept form is best when you know the slope and the yintercept .
Video Tutorial on Point Slope Form
Practice Problems
 Equation 1: 2x + 2y = 6
 Equation 2: y  5 = 3(x 2)
 Equation 3: y = 2x + 3
 Equation 4: y + 3 = 3(x  ½)
Equation 2 and equation 4 are the only ones in point slope form.
Equation 1 is in Standard Form
Equation 3 is in Slope intercept form
 Equation 1: y − 2 = 3(x − 4)
 Equation 2: y + 5 = (x − 4)
 Equation 3: y = 3(x − 4) + 2
 Equation 4: y − 2 = 3(x − 4)
Equation 1, 2 and equation 4 are the in point slope.
How to Solve common point slope form questions
Example 1
Write the point slope equation of a line with slope 3 that passes through the point (2,5)
Step 1Substitute slope for 'm' and the coordinates for x_{1} and y_{1} into the formula
 y − y_{1} = m(x − x_{1})
 y − 5 = 3(x − 2)
 y − 5 = 3(x + 2)
Yes, it really is that easy to write the equation of a line in point slope form when you know its slope and 1 point on the line! . This should be a real relief to those of you who are used to doing this with slope intercept form , which would require 2 more steps (i.e. substitute a point and solve for b').
Example 2
Find equation given 2 points
Write the point slope equation of a line that goes through the points (1,7) and (5,19)
Step 1Calculate the slope
m (slope) =
Step 2Substitute slope for 'm' and the coordinates for x_{1} and y_{1} into the formula (you can use either point)
 y − y_{1}= m(x − x_{1})
 y − 7 = 3(x − 1)
 y − 5 = 3(x − 19 )
Practice writing equations in point slope form
This problem is just like example 1 (find equation given 1 point and the slope)
Substitute slope for 'm' and the coordinates for x_{1} and y_{1} into the formula
 y − y_{1}= 5(x − x_{1})
 y − 4 = 3(x − 1 )
Write the point slope equation for the line in the graph below.
This problem is just like example 1 (find equation given 1 point and the slope)
Substitute slope for 'm' and the coordinates for x_{1} and y_{1} into the formula
 y − y_{1} = 3(x − x_{1})
 y − 7 = 3(x + 4)
This problem is just like example 2 (find equation through 2 points)
Step 1This problem is just like example 1 (find equation given 1 point and the slope)
Substitute slope for 'm' and the coordinates for x_{1} and y_{1} into the formula
 y − y_{1}= ½ (x − x_{1})
 y − 4 = 3(x − 3)
 y + 4 = 3(x − 3)
Other Types of Problems
There are a many other question types that involve point slope form. Try some of the ones below to see how you do.
Write the point slope equation for the line in the graph below.

Related Links:
 Equation of Line Formula
 Slope Intercept Form
 Worksheet on Point Slope Form of a line (pdf with answer key on this page's topic