Graphing in Slope-Intercept Form
I can graph a line from y = mx + b by plotting b first, then stepping by the slope.
The problem this sheet solves
Graphing from slope-intercept form fails at the START, not the stepping. A student who begins at the origin draws a line parallel to the right one, which is the kind of error that looks like carelessness and is actually a missing idea: the slope tells you how to move from a point you already have. Reading the form out of order is the other half, since in y = 6 − 3x the slope is −3 and b is 6. This sheet plots (0, b) first, every time, and treats the slope as a move from that point rather than from anywhere. The form itself is displayed on the page rather than described, and the sheet handles equations written out of order so students identify m and b by role instead of by position.
The key rule
In y = mx + b, plot (0, b) FIRST, then step by m to a second point and draw the line through both. The slope tells you how to move from a point you already have — never from the origin.
Start at b. Step by m.
Watch out
The mistake: To graph y = 5/3x + 4, a student starts at the origin and steps up 5, right 3.
The fix: The slope was right; the start was not. b = 4, so begin at (0, 4). Their line is parallel, 4 units low.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
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.