Learn on PengiBig Ideas Math, Course 2, AcceleratedChapter 3: Graphing and Writing Linear Equations

Lesson 6: Writing Equations in Slope-Intercept Form

In this Grade 7 lesson from Big Ideas Math Course 2 Accelerated, students learn how to write equations of lines in slope-intercept form (y = mx + b) by identifying the slope and y-intercept from a graph. The lesson covers interpreting the meaning of slope and y-intercept in real-world contexts, such as a car trip, and applies these skills to geometric figures like parallelograms. Aligned with Common Core Standard 8.EE.6, this lesson is part of Chapter 3 on Graphing and Writing Linear Equations.

Section 1

Writing an Equation from a Graph

Property

To write an equation from a graph in slope-intercept form $y = mx + b$ :

Identify the y-intercept $b$ where the line crosses the y-axis
Find the slope $m = \frac{\text{rise}}{\text{run}}$ using two clear points on the line
Substitute $m$ and $b$ into $y = mx + b$

Examples

Section 2

Horizontal lines have slope 0

Property

The slope of a horizontal line, $y = b$ , is 0.

Examples

Section 3

Real-World Meaning of Slope and Y-Intercept

Property

In a real-world context described by the equation $y = mx + b$ :

The slope ( $m$ ) represents the rate of change. It tells you how much the dependent variable ( $y$ ) changes for every one-unit increase in the independent variable ( $x$ ).
The y-intercept ( $b$ ) represents the initial value or starting point. It is the value of the dependent variable ( $y$ ) when the independent variable ( $x$ ) is zero.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Writing an Equation from a Graph

Property

To write an equation from a graph in slope-intercept form $y = mx + b$ :

Identify the y-intercept $b$ where the line crosses the y-axis
Find the slope $m = \frac{\text{rise}}{\text{run}}$ using two clear points on the line
Substitute $m$ and $b$ into $y = mx + b$

Examples

Section 2

Horizontal lines have slope 0

Property

The slope of a horizontal line, $y = b$ , is 0.

Examples

Section 3

Real-World Meaning of Slope and Y-Intercept

Property

In a real-world context described by the equation $y = mx + b$ :

The slope ( $m$ ) represents the rate of change. It tells you how much the dependent variable ( $y$ ) changes for every one-unit increase in the independent variable ( $x$ ).
The y-intercept ( $b$ ) represents the initial value or starting point. It is the value of the dependent variable ( $y$ ) when the independent variable ( $x$ ) is zero.

Examples

Overview

Lesson overview

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

Overview

Section 1

Writing an Equation from a Graph

Property

To write an equation from a graph in slope-intercept form $y = mx + b$ :

Identify the y-intercept $b$ where the line crosses the y-axis
Find the slope $m = \frac{\text{rise}}{\text{run}}$ using two clear points on the line
Substitute $m$ and $b$ into $y = mx + b$

Examples

Section 2

Horizontal lines have slope 0

Property

The slope of a horizontal line, $y = b$ , is 0.

Examples

Section 3

Real-World Meaning of Slope and Y-Intercept

Property

In a real-world context described by the equation $y = mx + b$ :

The slope ( $m$ ) represents the rate of change. It tells you how much the dependent variable ( $y$ ) changes for every one-unit increase in the independent variable ( $x$ ).
The y-intercept ( $b$ ) represents the initial value or starting point. It is the value of the dependent variable ( $y$ ) when the independent variable ( $x$ ) is zero.