Lesson 2: Solving by Graphing
Duration of Days: 3
Lesson Objective
Students will be able to estimate the solution to a system of two linear equations by graphing both equations on the same coordinate plane and identifying their point of intersection.
How do you accurately graph a system of equations to ensure the point of intersection is clear?
Why is graphing considered an "estimation" method for solving systems?
What does it mean if the lines in a system never intersect?
System of Linear Equations: Two or more linear equations that are dealt with at the same time.
Solution to a System: The ordered pair (x, y) that makes both equations true simultaneously.
Intersection: The specific point where the graphs of two linear equations meet.
Ordered Pair: A pair of numbers used to locate a specific point on a graph.
8.EE.C.8.A: Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs.
Target D.3: The student estimates solutions by graphing systems of two linear equations in two variables.
Description: This lesson focuses on the visual application of systems. Students will practice plotting multiple lines and identifying their common points.
Purpose: To provide a concrete, visual representation of what it means for a solution to satisfy two equations.
DOK Level: Level 2 (Basic Application) – Graphing systems and identifying points of intersection.
Inaccurate Graphing: Errors in slope or intercept can lead to an incorrect intersection point, emphasizing why this method is often called "estimating".
Parallel Lines: Thinking that parallel lines must eventually meet if the graph were larger.
Non-Integer Solutions: Difficulty identifying solutions that do not fall exactly on the grid's crosshairs.
Support: Provide Graphing Notes to help students who struggle with the basic mechanics of plotting lines.
Scaffolding: Have students first practice finding intersections before asking students to graph them.
Exit Tickets