# Lesson 10

On or Off the Line?

### Lesson Narrative

This lesson builds upon earlier work with linear equations in two variables in two types of contexts: contexts like distance versus time, where there is an initial value and a rate of change, and contexts like budgets, where there is an equation constraining the possible combinations of two quantities. In this lesson, students consider pairs of linear equations in each type of context and interpret the meaning of points on the graphs of the equations.

In the first activity, students are given two constraints on the number of nickels and dimes in someone's pocket: a constraint on the total value and a constraint on the total number of coins. In the second activity, students study two graphs that represent two different students producing locker signs at different rates. In each case students interpret the meaning of various points on and off the lines, including the point of intersection.

### Learning Goals

Teacher Facing

• Determine (in writing) a point that satisfies two relationships simultaneously, using tables or graphs.
• Interpret (orally and in writing) points that lie on one, both, or neither line on a graph of two simultaneous equations in context.

### Student Facing

Let’s interpret the meaning of points in a coordinate plane.

### Student Facing

• I can identify ordered pairs that are solutions to an equation.
• I can interpret ordered pairs that are solutions to an equation.