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:

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

Standard Form Equation of Line

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.

Standard form equation of line

$ \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
$$ 3x + 5y = 3 $$ $$ 2y = 4x + 2 $$
$$ 2x - y = 6 $$ $$ x = 6 - y $$
$$ -2x + y = 7 $$ $$ y = 2x + 7 $$

Video Tutorial on Standard Form Equation of a Line

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 Example 0 1

How to find the y-intercept:

Set x = 0 3(0) + 2y = 6
Solve for y Example 0 2

How to Graph from Standard Form

Example 2

Plot the x and y-intercepts and draw the line on the graph paper!

Standard form equation of line

Practice Problems

Problem 1

Identify which equations belowon the right 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 belowon the right 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

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:

Example problem 1
Step 3

Set x = 0:

2(0) + 3y = 18
Step 4

Solve for y:

Example problem 1B
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:

Problem 2A
Step 3

Set x = 0:

3(0) + 5y = 15
Step 4

Solve for y:

Problem 2B
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 5

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:

Problem 3A
Step 3

Set x = 0:

3y − 2(0) = -12
Step 4

Solve for y:

Problem 3B
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
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