Converting Between Forms of Linear Equations
I can rewrite a linear equation in any of the three forms without changing the line.
The problem this sheet solves
Going from y = (3/4)x − 2 to standard form, the multiplier has to reach the constant as well, and it usually does not. The result is a different line that looks properly converted. The second issue is knowing when to stop, since standard form is not finished while a fraction remains in it. This sheet treats converting as rewriting the SAME line, and it builds in a one-point check so a broken conversion is caught by the student rather than the teacher. Every term gets the multiplier, the constant included, and the sheet is explicit about what finished looks like in each form.
The key rule
Changing the form never changes the line. Standard form is not finished while a fraction is in it: multiply EVERY term, the constant included, then check one point.
Every term, not just the fraction.
Watch out
The mistake: Converting y = 3/4x − 2 to standard form, a student multiplies by 4 and writes 3x − 4y = 2.
The fix: Every term gets the 4, the constant included: 4y = 3x − 8, so 3x − 4y = 8. Check x = 0: −4y = 8 gives y = −2, which matches.
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.