Solving Equations Graphically
I can solve an equation by graphing both sides and reading the x where they cross.
What students learn
Students learn to solve an equation by graphing each side as a line and reading the x of the crossing, then test it in both sides.
See inside
The key rule
Go straight up or down from the crossing to the x-axis: that x is the solution. Then check it in both sides.
crossing (a, b): x = a
The y-value tells what both sides equal; the equation asked for x.
Watch out
Graphed, the sides of 2x + 1 = x + 4 cross at (3, 7). A student says x = 7.
The mistake: x = 7: the crossing's y7 is what both sides equal, not the input.
The fix: x = 3: 2(3) + 1 = 7 = 3 + 4The solution is the crossing's x.
The mistakes it targets
- Answers with the crossing's y-value instead of its x-value
- Swaps the x- and y-coordinates of the crossing
- Gives the whole point as the solution of a one-variable equation
- Stops before finding the y-value of the crossing point
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.