# 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:

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

### 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.

$\text{X Intercept: } \\ \frac C A = \frac 6 3 = 2$

$\text{Y Intercept: } \\ \frac C B = \frac 6 2 = 3$

#### Example and Non Example Equations

 Examples of Standard Form Non-Examples $$3x + 5y = 3$$ $$2y = 4x + 2$$ $$2x - y = 6$$ $$x = 6 - y$$ $$-2x + y = 7$$ $$y = 2x + 7$$

### Sample Practice Problems

##### 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!

### 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 -$$\frac 1 2$$ y = 11

Equation 2 and equation 4 are the only ones in standard form.

Equation 3 is in Slope intercept form.

##### 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: $$\frac 1 2$$ y − 4x = 0

Equation 1 and equation 4 are the only ones in standard form.

Equation 3 is in point slope form.

##### Problem 3
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!

##### Problem 4
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!

##### Problem 5
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!