# 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: $Ax + By = C \\ A \ne 0 \\ b \ne 0$

#### 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

### 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!

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 $$### Practice Problems • Equation 1: 2x + 5 = 2y • Equation 2: 2x + 3y = 4 • Equation 3: y =2x + 3 • Equation 4: 4x -$$ \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

Step 1

Set y = 0

2x + 3(0) = 18
Step 2

Solve for x

Step 3

Set x = 0

2(0) + 3y = 18
Step 4

Solve for y

Graph

Plot the x and y-intercepts, which in this case is (9,0) and (0,6) and draw the line on the graph paper!

Step 1

Set y = 0

3x + 5(0) = 15
Step 2

Solve for x

Step 3

Set x = 0

3(0) + 5y = 15
Step 4

Solve for y

Graph

Plot the x and y-intercepts, which in this case is (5,0) and (0,3) and draw the line on the graph paper!

Step 1

Set y = 0

3(0) − 2x = -12
Step 2

Solve for x

Step 3

Set x = 0

3y − 2(0) = -12
Step 4

Solve for y

Graph

Plot the x and y-intercepts, which in this case is (6,0) and (0,-4) and then graph the equation!

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