From Graphs to Substitution: Finding the Break-Even Point
Shared by A STEM Educator
Students will be able to solve a system of two linear equations using substitution, interpret the solution as a coordinate point in context, and verify the solution by graphing — addressing HSA-REI.C.6.
Lesson Overview
Students begin by visually identifying intersection points of two lines on a coordinate plane, then bridge to algebraic substitution through a financial literacy context involving phone plans and spending comparisons. The progression moves from graphing → reading intersections → interpreting meaning → discovering substitution → solving and verifying algebraically.
Materials
- Vertical whiteboards or chart paper
- Dry-erase markers (multiple colors)
- Random grouping tool
- Graphing calculators or Desmos access (optional, for verification)
- Rulers or straightedges
Scaffolded Task Progression
(a) At how many texts do both plans cost the same?(b) For 100 texts, which plan is cheaper?(c) For 300 texts, which plan is cheaper? [ Interactive graph / diagram — available in the full lesson ]
(a) What does the number 200 mean in this situation?(b) What does the number 50 mean in this situation?(c) Write one complete sentence explaining what the intersection point tells someone choosing between Plan A and Plan B.
Unlock the full lesson
See all 5 scaffolded tasks, the full answer key, warm-up, exit slip, and a print-ready version — free to start.
Create a free accountAlready have an account? Sign in
Like this lesson but want to tweak it?
Make an editable copy and adjust the tasks, warm-up, and answer key to fit your class — no need to start from scratch.