Writing Equations in Slope-Intercept Form
I can write y = mx + b for a line by reading b off the y-axis and counting the slope.
The problem this sheet solves
Writing an equation from a graph fails on WHICH intercept b is. A student who takes the x-intercept produces an equation with the correct slope and a constant belonging to a different line entirely, and because both numbers genuinely appear on the picture, nothing about the choice feels like a guess. It is a quiet error and it survives otherwise perfect work. This sheet ties b to the y-AXIS crossing explicitly and says plainly that the x-intercept never enters the equation, which is the sentence that settles it. Slope is counted between exact grid points, and the sheet runs graph to equation only, so students practise the direction that is genuinely harder.
The key rule
Read b where the line crosses the y-AXIS, count m between two exact grid points, then write y = mx + b. The x-intercept is a different number and never appears in the equation.
b comes off the y-axis. Only the y-axis.
Watch out
The mistake: A line crosses the x-axis at 8 and the y-axis at −3. A student writes y = 3/8x + 8.
The fix: Both numbers are on the graph, but b is the y-axis one: −3. The equation is y = 3/8x − 3.
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.