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

Lesson 1: Graphing Linear Equations

In this Grade 7 lesson from Big Ideas Math, Course 2 Accelerated, students learn how to graph linear equations by generating solution points from a table of values and plotting them on a coordinate grid. Students explore the relationship between equations in the form y = ax + b and their graphs, discovering that every point on a line is a solution to its corresponding linear equation. The lesson also introduces using a graphing calculator to graph linear equations and interpret viewing window settings.

Section 1

Solutions of an equation and its graph

Property

The graph of a linear equation $Ax + By = C$ is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.

Examples

Is the point $(2, 7)$ a solution to the equation $y = 3x + 1$ ? Yes, because substituting the values gives $7 = 3(2) + 1$ , which simplifies to $7 = 7$ . The point is on the line.

Is the point $(1, 3)$ a solution to the equation $y = 3x + 1$ ? No, because substituting the values gives $3 = 3(1) + 1$ , which simplifies to $3 = 4$ . This is false, so the point is not on the line.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Solutions of an equation and its graph

Property

The graph of a linear equation $Ax + By = C$ is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.

Examples

Is the point $(2, 7)$ a solution to the equation $y = 3x + 1$ ? Yes, because substituting the values gives $7 = 3(2) + 1$ , which simplifies to $7 = 7$ . The point is on the line.

Is the point $(1, 3)$ a solution to the equation $y = 3x + 1$ ? No, because substituting the values gives $3 = 3(1) + 1$ , which simplifies to $3 = 4$ . This is false, so the point is not on the line.

Overview

Lesson overview

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

Overview

Section 1

Solutions of an equation and its graph

Property

The graph of a linear equation $Ax + By = C$ is a straight line. Every point on the line is a solution of the equation. Every solution of this equation is a point on this line.

Examples

Is the point $(2, 7)$ a solution to the equation $y = 3x + 1$ ? Yes, because substituting the values gives $7 = 3(2) + 1$ , which simplifies to $7 = 7$ . The point is on the line.

Is the point $(1, 3)$ a solution to the equation $y = 3x + 1$ ? No, because substituting the values gives $3 = 3(1) + 1$ , which simplifies to $3 = 4$ . This is false, so the point is not on the line.