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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 topic-point 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 Equations

 Examples of Point Slope Form Equations Non-Examples 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 are other forms more useful?

• Standard Form is more convenient when you know or need to know the x intercept and also the y-intercept and do not know the slope
• Slope intercept form is best when you know the slope and the y-intercept .
• Video Tutorial on Point Slope Form
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Practice Problems

Problem 1) Identify which equations below are in point slope form
• Equation 1: 2x + 2y =6
• Equation 2: y - 5 = 3(x -2)
• Equation 3: y =2x + 3
• Equation 4: y + 3 = 3(x - ½)

Problem 2) Which equations below are in point slope 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)

How to Solve common point slope form questions
Example 1: Find equation given slope and 1 point
Write the point slope equation of a line with slope 3 that passes through the point (-2, 5).
 1)Substitute slope for 'm' and the coordinates for x1 and y1 into the formula y − y1= m(x − x1) 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 ) .
 1) Calculate the slope m (slope) = 2) Substitute slope for 'm' and the coordinates for x1 and y1 into the formula (you can use either point) y − y1= m(x − x1) y − 7 = 3(x − 1 ) Or if you use the 2nd point y − 5 = 3(x − 19 )
Practice writing equations in point slope form

Problem 1)Write the point slope equation of a line that has a slope of 5 and that goes through the point (1, 4).

Write the point slope equation for the line in the graph below.
 Step 1

Practice writing equations in point slope form

Problem 1)Write the point slope equation of a line that has a slope of -3and that goes through the point (-4, 7).

Problem 2) Write the point slope equation of a line that goes through the points (2, 6) and ( 4, 7).

Problem 3) Write the point slope equation of a line that has a slope of ½ and that goes through the point (3, −4).