Standard Form and Graphing with Intercepts
I can find both intercepts of Ax + By = C and graph the line through them.
What students learn
Students learn to find the intercepts of Ax + By = C by setting the other variable to 0, write them as points and graph the line through them.
See inside
The key rule
Set the other variable to 0. Don't stop at C: divide it by the coefficient left.
set y = 0, then x = 0
2x + 7y = 14 crosses the y-axis at 2, not at 14.
Watch out
Find the y-intercept of 3x + 5y = 30.
The mistake: the y-intercept is 3030 is C, the total; nothing was divided.
The fix: 5y = 30, so (0, 6)Set x = 0, then divide by 5.
The mistakes it targets
- Reads the constant C as an intercept
- Drops the sign of a negative y coefficient
- Writes an intercept's coordinates in the wrong order
- Graphs from one intercept only, or through the constant
The interactive Teacher Deck (31 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 (three 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.