Lesson objective: Apply graphs to solve systems of equations with a real-world context.

This lesson provides an opportunity for students to apply their knowledge and understanding of graphs and systems of equations to a real-life situation. Students are asked to construct a graph to show which hikers meet on a trail given different clues.

Key Concept students will use:

- A point of interesection represents a solution to a system of equations.

Skills students will use:

- Construct a graph of a linear function (Unit 7).
- Interpret points on the graph representing a real-world situation (Unit 6).
- Understand a solution to a system as an ordered pair where two conditions are true at the same time.

Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they make sense of multiple relationships in a problem and the connection between the relationships. Students will use a graph to represent the relationships and interpret features such as intersection points and parallel lines in the context of a real-world situation.

**Key vocabulary: **

- intersection
- parallel
- slope
- y-intercept

**Special materials needed:**

- graph paper or graphing technology