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A+ A− B

Standard Form Equation of a line

Examples of equation and Graphs

Standard Form Equation of Line 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

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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
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    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

    Slope Intercept Form
    Point Slope Form
    Standard Form
    Toggle Points
    Slope?
    Show Rise and Run ?
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    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
    Answer
    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
    Answer
    Problem 3) Find the intercepts and then graph the following equation
    2x + 3y = 18
    First Steps
    Problem 4) Find the intercepts and then graph the following equation
    3x + 5y = 15
    First Steps
    Problem 6) Find the intercepts and then graph the following equation
    3y − 2x = -12
    First Steps