Lesson objective: Understand that a point of intersection between two lines on a graph represents a solution to a system of the two equations.

Students bring prior knowledge of graphing functions and linear equations from 8.F.A.1 and 8.F.B.4. This prior knowledge is extended to representing a system of equations on a graph as students connect parallel lines, coinciding lines, or points of intersection to solutions of a system. A conceptual challenge students may encounter is thinking that if two non-parallel lines do not meet in a graphing window, then the system does not have a solution.

The concept is developed through work with graphs, which visually represents all solutions to linear equations as a line.

This work helps students deepen their understanding of equivalence because a point of intersection shows where two equations 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 a point of intersection as an ordered pair that makes both equations true in a system of equations.

**Key vocabulary:**

- intersection
- parallel

**Special materials needed:**

- graph paper and/or graphing technology