Standard Form Equation of a line

Examples of equation and Graphs

Overview of different forms of a line's equation

Standard Form Equation of 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

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 are other forms more useful?

Video Tutorial

on Standard Form Equation of a Line

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

Example2
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 =

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 - ½y = 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: ½y − 4x = 0

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

Graph of Standard Form Equation
Problem 4

Find the intercepts and then graph the following equation 3x + 5y = 15

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!

Graph of Standard Form Equation
Problem 4

Find the intercepts and then graph the following equation 3y − 2x = -12

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!

Graph of Standard Form Equation
Next Convert to Slope Intercept Form