Learn on PengiBig Ideas Math, Course 3Chapter 4: Graphing and Writing Linear Equations

Lesson 5: Graphing Linear Equations in Standard Form

In this Grade 8 lesson from Big Ideas Math, Course 3 (Chapter 4), students learn to graph linear equations written in standard form (ax + by = c) using two methods: converting to slope-intercept form and using x- and y-intercepts. Real-world scenarios, such as selling concert tickets or buying cheese, help students understand how to write and interpret standard form equations on a coordinate plane.

Section 1

Linear equation in two variables

Property

An equation of the form $Ax + By = C$ , where $A$ and $B$ are not both zero, is called a linear equation in two variables.

A linear equation is in standard form when it is written $Ax + By = C$ .

An ordered pair $(x, y)$ is a solution of the linear equation $Ax + By = C$ , if the equation is a true statement when the $x$ - and $y$ -values of the ordered pair are substituted into the equation.

Section 2

Converting Linear Equations to Slope-Intercept Form

Property

To convert a linear equation to slope-intercept form $y = mx + b$ , solve the equation for $y$ by isolating $y$ on one side of the equation.

Examples

Section 3

Graphing Linear Equations Using Intercepts

Property

To graph a linear equation using the intercepts:
Step 1. Find the $x$ -intercept by setting $y = 0$ and solving for $x$ .
Step 2. Find the $y$ -intercept by setting $x = 0$ and solving for $y$ .
Step 3. Plot both intercepts on the coordinate plane.
Step 4. Draw a straight line through the two points.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Linear equation in two variables

Property

An equation of the form $Ax + By = C$ , where $A$ and $B$ are not both zero, is called a linear equation in two variables.

A linear equation is in standard form when it is written $Ax + By = C$ .

Section 2

Converting Linear Equations to Slope-Intercept Form

Property

To convert a linear equation to slope-intercept form $y = mx + b$ , solve the equation for $y$ by isolating $y$ on one side of the equation.

Examples

Section 3

Graphing Linear Equations Using Intercepts

Property

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Linear equation in two variables

Property

An equation of the form $Ax + By = C$ , where $A$ and $B$ are not both zero, is called a linear equation in two variables.

A linear equation is in standard form when it is written $Ax + By = C$ .

Section 2

Converting Linear Equations to Slope-Intercept Form

Property

To convert a linear equation to slope-intercept form $y = mx + b$ , solve the equation for $y$ by isolating $y$ on one side of the equation.