A line crosses the y-axis at 3 and rises 1 for every run of 2.
Show answer
y = ½x + 3
Free printable worksheet
Writing Equations from Graphs Worksheet
Nine plotted lines for practicing slope, intercepts, and writing equations from visual information.
Algebra 1Grades 7-104 pagesAnswer key included
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What this worksheet includes
- Nine plotted lines for practicing slope, intercepts, and writing equations from visual information.
- 4-page printable PDF with a complete answer key
- Designed for Grades 7-10 algebra 1 practice
- Available as an immediate free download with no email required
How to use it
Use this writing equations from graphs worksheet for guided practice, independent review, homework, tutoring sessions, or a quick skills check. The spacious layout is designed to leave room for students to show their work rather than guess from crowded answer choices.
After students finish, compare their reasoning with the included answer key. When an answer is incorrect, have the student locate the first step where their work changed direction before trying the problem again.
Who this practice is for
This resource is designed for grades 7-10 students working on algebra 1. Teachers, tutors, homeschool families, and parents can preview the first page before deciding whether the level and spacing fit the student.
Looking for a broader sequence? Browse all Algebra I worksheets.
Topic guide
How to approach writing equations from graphs
Writing an equation from a graph requires translating visual information into slope and intercept. Choose two points that land exactly on grid intersections, calculate rise over run, and then determine the y-intercept.
The graphs include positive, negative, and fractional slopes. Students should verify each equation by substituting a second visible point rather than relying on the line's appearance alone.
Learning objectives
- Calculate slope from two points on a graph
- Identify the y-intercept from a plotted line
- Write and verify an equation in slope-intercept form
Skills to review first
- Reading ordered pairs
- Simplifying fractions
- Slope-intercept form
Worked example
Follow the reasoning step by step
A line passes through (0, −2) and (3, 4). Write its equation.
- Find the slope: m = (4 − (−2)) ÷ (3 − 0) = 6 ÷ 3 = 2.
- Read the y-intercept from (0, −2): b = −2.
- Substitute m and b into y = mx + b.
- Check (3, 4): 4 = 2(3) − 2.
Solution: y = 2x − 2.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
A line passes through (0, 5) and (2, 1).
Show answer
y = −2x + 5
A horizontal line passes through (−4, −3).
Show answer
y = −3
Error check
Common mistakes to watch for
- Using run over rise instead of rise over run
- Estimating points that do not fall on grid intersections
- Reading the x-intercept as b in y = mx + b