Standard Form Equation of a line

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

$ \text : \\ Ax + By = C \\ A \ne 0 \\ B \ne 0 $

General Formula for x and y-intercepts

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

$ \text \\ \frac C A = \frac 6 3 = 2 $

$ \text \\ \frac C B = \frac 6 2 = 3 $

Example and Non Example Equations

When is standard form useful?

• When you want to graph the line.
• When you know the y-intercept of the line.
• When you 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.