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 \\ A \ne 0 \\ b \ne 0 $
Example and Non Example Equations
Examples of Standard Form Equations  NonExamples 
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 yintercept of the line
 When you want to know the x intercept
 Contrast this with slope intercept form in this case, you have to do more work to find 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
Examples
Examples of Standard Form
Example 1
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
Example 2
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 $$ where where $$ A \ne 0 $$ and $$ B \ne 0$$, you can use the formulas below to find the x and yintercepts.
The xintercept =$$ \frac C A = \frac 6 3 =2 $$
The yintercept =$$ \frac C B = \frac 6 2 = 3 $$
Practice Problems
 Equation 1: 2x + 5 = 2y
 Equation 2: 2x + 3y = 4
 Equation 3: y =2x + 3
 Equation 4: 4x $$ \frac 1 2 $$ y = 11
Equation 2 and equation 4 are the only ones in standard form.
Equation 3 is in Slope intercept form
 Equation 1: 11 = ¼x + ½y
 Equation 2: 2x + 5 + 2y = 3
 Equation 3: y  2 = 3(x − 4)
 Equation 4: $$ \frac 1 2 $$ y − 4x = 0
Equation 1 and equation 4 are the only ones in standard form.
Equation 3 is in point slope form
Set y = 0
Solve for x
Set x = 0
Solve for y
Plot the x and yintercepts, which in this case is (9,0) and (0,6) and draw the line on the graph paper!
Set y = 0
Solve for x
Set x = 0
Solve for y
Plot the x and yintercepts, which in this case is (5,0) and (0,3) and draw the line on the graph paper!
Set y = 0
Solve for x
Set x = 0
Solve for y
Plot the x and yintercepts, which in this case is (6,0) and (0,4) and then graph the equation!

Related Links:
 Linear Equations
 Equation of Line Formula
 Slope Intercept Form
 Slope Intercept to Standard Form
 Point Slope to Standard Form
 Worksheet on standard form equation(pdf with answer key on this page's topic)