Ticket Sales & Standard Form: Intercepts, Cover-Up, and the Power of Ax + By = C
Shared by A STEM Educator
Students will write linear equations in Standard Form (Ax + By = C), identify the meaning of coefficients and the constant term in context, calculate x- and y-intercepts using the cover-up method, and graph lines using intercepts.
Lesson Overview
Students begin with a real-world ticket-sales scenario to discover Standard Form organically, then thin-slice through intercept calculations using the cover-up method, graphing, negative coefficients, and generalizing the structure of Ax + By = C.
Materials
- Vertical whiteboards or large chart paper (one per group)
- Dry-erase markers (one per group)
- Erasers or paper towels
- Random grouping cards or app
- Projector for Desmos activity
- Student devices or shared device for Desmos (Part 3)
- Four-Quadrant note-taking template (half-sheet, one per student)
Scaffolded Task Progression
Your school is selling tickets to a talent show. Student tickets cost $5 each and adult tickets cost $10 each. The school needs to make exactly $100 in ticket sales tonight.
- If they sell 0 adult tickets, how many student tickets do they need to sell?
- If they sell 0 student tickets, how many adult tickets do they need to sell?
- Find 3 other combinations of student and adult tickets that hit the target exactly.
\nRecord all combinations in a table on your board.
Plot all your ticket combinations from Task 1 on a coordinate grid. Put student tickets () on the horizontal axis and adult tickets () on the vertical axis.
- Label both axes with units.
- Connect the points.
- What shape do you get? What does that tell you?
[ Interactive graph / diagram — available in the full lesson ]
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