Slope 2 through (1, 5)
Show answer
y − 5 = 2(x − 1)
Free printable worksheet
Point-Slope Form Worksheet
Twenty point-and-slope prompts for writing accurate equations in point-slope form.
Algebra 1Grades 7-103 pagesAnswer key included
No email is required. Download the complete worksheet and answer key now.
Download the free PDF
What this worksheet includes
- Twenty point-and-slope prompts for writing accurate equations in point-slope form.
- 3-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 point-slope form 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 point-slope form
Point-slope form, y − y₁ = m(x − x₁), builds a linear equation from one known point and a slope. It is especially useful when the graph's y-intercept is not immediately available.
The signs inside the parentheses come from subtracting the point's coordinates. A negative coordinate therefore creates a plus sign, such as y − (−2) becoming y + 2.
Learning objectives
- Substitute a point and slope into point-slope form
- Handle negative coordinates correctly
- Convert point-slope form to slope-intercept form
Skills to review first
- Slope between two points
- Substitution
- Distributing and simplifying
Worked example
Follow the reasoning step by step
Write the equation of the line with slope 4 through (3, −2).
- Start with y − y₁ = m(x − x₁).
- Substitute m = 4, x₁ = 3, and y₁ = −2.
- Simplify y − (−2) to y + 2.
- Write y + 2 = 4(x − 3).
Solution: Point-slope form: y + 2 = 4(x − 3); slope-intercept form: y = 4x − 14.
Try before downloading
Three sample problems
Work each problem, then open the answer to check your result.
Slope −3 through (−2, 4)
Show answer
y − 4 = −3(x + 2)
Through (−1, 2) and (3, 10)
Show answer
m = 2; y − 2 = 2(x + 1)
Error check
Common mistakes to watch for
- Switching the x- and y-coordinates
- Copying a negative coordinate without subtracting it
- Using different points to calculate and substitute the slope inconsistently