Standard Form Equation of a 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

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

• 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.

Video Tutorial on Standard Form Equation of a Line

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 =

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

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: ½y − 4x = 0

Answer

Equation 1 and equation 4 are the only ones in standard form.
Equation 3 is in point slope form.

Problem 3) Find the intercepts and then graph the following equation

2x + 3y = 18

First Steps

First, find the intercepts by setting y and then x equal to zero. This is pretty straightforward since the line is already in standard form.

Set y = 0	2x + 3(0) = 18
Solve for x
Set x = 0	2(0) + 3y = 18
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) Find the intercepts and then graph the following equation

3x + 5y = 15

First Steps

Set y = 0	3x + 5(0) = 15
Solve for x
Set x = 0	3(0) + 5y = 15
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) Find the intercepts and then graph the following standard form equation

4y - 5x = 25

First Steps

Set y = 0	4(0) - 5x = 25
Solve for x
Set x = 0	4y - 5(0) = 20
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 6) Find the intercepts and then graph the following equation

3y − 2x = -12

First Steps

Set y = 0	3(0) − 2x = -12
Solve for x
Set x = 0	3y − 2(0) = -12
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!