Graphing Linear Equations (Standard Form) | Luna Learn 24

Graphing Linear Equations (Standard Form)

This lesson focuses on graphing linear equations in standard form. The standard form of a linear equation is given by Ax + By = C, where A, B, and C are constants. This method requires converting the equation to slope-intercept form or using intercepts to graph the line.

Outline

Introduction to Standard Form
Converting Standard Form to Slope-Intercept Form
Using Intercepts to Graph Linear Equations
Examples of Graphing Linear Equations in Standard Form
Exercises with Solutions
Homework
Revision Section
Contact Us for Tutoring

Standard Form Overview

The standard form of a linear equation is Ax + By = C. To graph a line from this form:

Find the x-intercept by setting y = 0 and solving for x.
Find the y-intercept by setting x = 0 and solving for y.
Plot these intercepts on the graph and draw the line through them.

Examples of Graphing Linear Equations

Example 1:

Graph the equation 2x + 3y = 6.

Example 2:

Graph the equation -x + 2y = 4.

Example 3:

Graph the equation 3x - y = 9.

Example 4:

Graph the equation -2x + 4y = 8.

Example 5:

Graph the equation 4x + y = 12.

Example 6:

Graph the equation x - 3y = -3.

Exercises

Exercise 1:

Graph the equation 2x - y = 4.

Exercise 2:

Graph the equation -3x + 5y = 15.

Exercise 3:

Graph the equation 4x + 2y = 10.

Exercise 4:

Graph the equation -x + 3y = 6.

Exercise 5:

Graph the equation 5x - 2y = 8.

Exercise 6:

Graph the equation x + 4y = 12.

Solutions

Solution 1:

For 2x - y = 4: Find the intercepts and plot them.

Solution 2:

For -3x + 5y = 15: Find the intercepts and plot them.

Solution 3:

For 4x + 2y = 10: Find the intercepts and plot them.

Solution 4:

For -x + 3y = 6: Find the intercepts and plot them.

Solution 5:

For 5x - 2y = 8: Find the intercepts and plot them.

Solution 6:

For x + 4y = 12: Find the intercepts and plot them.

Homework

Graph the following equations: 2x + y = 5, -x + 4y = 8, 3x - 2y = 6.
Label the intercepts and draw each line.
Write a brief explanation of how to convert a standard form equation to slope-intercept form.

Revision

Review the following concepts:

The standard form of a linear equation Ax + By = C and how to graph it.
Finding x- and y-intercepts from the standard form equation.
Converting standard form to slope-intercept form for graphing.

Watch the Video Tutorial

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