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||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 are other forms more useful?
Video Tutorialon Standard Form Equation of a Line
Examples 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 $$ where where $$ A \ne 0 $$ and $$ B \ne 0$$, you can use the formulas below to find the x and y-intercepts.
The x-intercept =$$ \frac C A = \frac 6 3 =2 $$
The y-intercept =$$ \frac C B = \frac 6 2 = 3 $$
- Equation 1: 2x + 5 = 2y
- Equation 2: 2x + 3y = 4
- Equation 3: y =2x + 3
- Equation 4: 4x -$$ \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