# Lesson 5

Equations and Their Graphs

### Lesson Narrative

So far in the unit, students have primarily used descriptions, expressions, and equations to represent relationships and constraints. In this lesson, they revisit the idea that graphs can be a useful way to represent relationships. Students are reminded that each point on a graph is a solution to an equation the graph represents. They analyze points on and off a graph and interpret them in context. In explaining correspondences between equations, verbal descriptions, and graphs, students hone their skill at making sense of problems (MP1).

In this lesson, students are also introduced to the use of graphing technology to graph equations.  This introduction could happen independently as long as it precedes the second activity in the lesson.

### Learning Goals

Teacher Facing

• Comprehend that the graph of a linear equation in two variables represents all pairs of values that are solutions to the equation.
• Interpret points on a graph of a linear equation to answer questions about the quantities in context.
• Use graphing technology to graph linear equations and identify solutions to the equations.

### Student Facing

• Let’s graph equations in two variables.

### Required Preparation

Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (If students typically access the digital version of the materials, Desmos is always available under Math Tools.)

### Student Facing

• I can use graphing technology to graph linear equations and identify solutions to the equations.
• I understand how the coordinates of the points on the graph of a linear equation are related to the equation.
• When given the graph of a linear equation, I can explain the meaning of the points on the graph in terms of the situation it represents.

Building On

### Glossary Entries

• constraint

A limitation on the possible values of variables in a model, often expressed by an equation or inequality or by specifying that the value must be an integer. For example, distance above the ground $$d$$, in meters, might be constrained to be non-negative, expressed by $$d \ge 0$$.

• model

A mathematical or statistical representation of a problem from science, technology, engineering, work, or everyday life, used to solve problems and make decisions.

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