Point-Slope Form
I can write the equation of a line in point-slope form from one point and the slope.
The problem this sheet solves
For the point (5, −3) with slope 2, the equation is y + 3 = 2(x − 5), and almost every student writes y − 3. The form subtracts y-sub-one, and y minus negative three is y plus three. It is a quiet error: the slope is untouched, the bracket is often perfect, and the page looks finished. This sheet makes the built-in subtraction the thing students watch for, and it deliberately mixes positive and negative coordinates so the sign flip cannot be handled by pattern. It also explains why this form exists at all: any point on the line will do, and no y-intercept is needed, which is exactly when slope-intercept form is the wrong tool.
The key rule
Substitute into y − y₁ = m(x − x₁) with the subtraction already there. A negative coordinate flips to a plus: (5, −3) gives y + 3, not y − 3.
The form subtracts. A minus coordinate comes out as a plus.
Watch out
The mistake: For the point (5, −3) with slope 2, a student writes y − 3 = 2(x − 5).
The fix: y₁ is −3, and y − (−3) is y + 3. The equation is y + 3 = 2(x − 5).
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.