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# Standard Form Equation of a line

## Examples of equation and Graphs

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 , point slope form and also this page's topic. Each one expresses the equation of a line, and each one has its own pros and cons. For instance, point slope form makes it easy to find the line's equation when you only know the slope and a single point on the line. Standard form also has some distinct uses, but more on that later.
Definition of Standard form Equation

The Standard Form equation of a line has the following formula: Ax + By = C where A ≠0 and B ≠0
Example and Non Example Equations

 Examples of Standard Form Equations Non-Examples 3x + 5y = 3 2y = 4x +2 2x − y =6 x = 6 − y -2x + y = 7 y = 2x + 7

## When is standard form useful?

• When you want to graph the line
• When you want to know the y-intercept of the line
• When you want to know the x intercept
• ## When are other forms more useful?

• Slope intercept form and point slope make it easier to find the slope of your line. In standard form, you must do some work to get the slope.
• Point slope makes it easy to graph the line when you only know the line's slope and a single point or when you know 2 points on the line.
• Video Tutorial on Standard Form Equation of a Line

## Standard Form Applet

 Toggle Points Show Rise and Run ?
  

Example 1 of Standard Form

Find the intercepts and graph the following equation:
3x + 2y = 6
How to find the x intercept .
 Set y = 0 3x + 2(0) = 6 Solve for x
How to find the y -intercept:
 Set x = 0 3(0) + 2y = 6 Solve for y

How to Graph from Standard Form.:
 Plot the x and y intercepts and draw the line on the graph paper!
General Formula for x and y intercepts

For the equation of a line in the standard form, Ax + By = C where A ≠0 and B ≠0 , you can use the formulas below to find the x and y-intercepts.

The x-intercept =
The y-intercept =
Practice Problems

Problem 1) Identify which equations below are in standard form
• Equation 1: 2x + 5 = 2y
• Equation 2: 2x + 3y = 4
• Equation 3: y =2x + 3
• Equation 4: 4x - ½y = 11
Problem 2) Identify which equations below are in standard form
• Equation 1: 11 = ¼x + ½y
• Equation 2: 2x + 5 + 2y = 3
• Equation 3: y - 2 = 3(x − 4)
• Equation 4: ½y − 4x = 0