Finding Equations: Error Analysis & Misconceptions
Mathematics
Grade 8
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on finding the equations of lines, especially perpendicular lines, designed to address common misconceptions and errors for Grade 8 students.
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Finding Equations: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
Name:
Date:
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Solve the following questions to practice finding line equations. Show your working in the grid spaces provided.
1.
Find the equation of the line passing through the point (2, 3) with a slope of 4.
[2 marks]2.
Determine the equation of the line that passes through (1, -2) and has a slope of -1/2.
[2 marks]3.
Construct the equation of a line perpendicular to y = 3x + 2 passing through (4, 5).
[3 marks]4.
A line has the equation y = -2x + 7. Find the equation of a line perpendicular to it passing through (0, 4).
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step problems, explaining your reasoning.
1.
A line passing through (3, 2) has an unknown slope. Its perpendicular line passes through (3, 2) and has a slope of 2. Find the equation of the original line.
[4 marks]2.
Given the line y = 1/2x - 4, find the equation of a line perpendicular to it passing through the point (-1, 3).
[3 marks]C
Real-world Applications
Solve these contextual problems involving finding line equations.
1.
A city planner wants to design a road perpendicular to an existing road that runs y = 2x + 5. If the new road must pass through the point (6, 2), what is its equation?
[3 marks]D
Challenge & Extension
Attempt these more difficult problems to extend your understanding.
1.
Find the equation of a line perpendicular to y = -3x + 1 that passes through the point (-4, 5). Then, verify if the lines are indeed perpendicular.
[4 marks]E
Mixed Review
Answer a variety of questions to review your skills on finding equations.
1.
What is the slope of a line perpendicular to y = -4x + 6?
[1 mark]2.
Construct the equation of a line passing through (0, 0) with a slope of 3/4.
[2 marks]F
Error Analysis & Misconceptions
Below are common mistakes made when finding equations of perpendicular lines. Review and correct the errors.
1.
A student states that the perpendicular line to y = 5x + 2 passing through (1, 4) is y = -5x + 1. Identify and explain the mistake.
[3 marks]2.
A student finds the line passing through (2, 3) with a slope of 2, then claims a perpendicular line is y = -2x + 1. Is this correct? Why or why not?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet