Finding Equations: Challenge & Extension
Mathematics
Year 9
17 questions
~34 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focused on finding equations of lines parallel to given lines, including real-world and extension problems.
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Finding Equations: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Date:
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Given the line y = 3x + 2, find the equation of the line parallel to it passing through the point (4, -1).
[3 marks]2.
Calculate the equation of a line parallel to 2x - y = 5 that passes through (0, 4).
[3 marks]3.
Write the equation of the line parallel to y = -x + 7, passing through the point (-3, 2).
[3 marks]4.
Determine the equation of the line parallel to y = 0.5x - 4 that passes through (2, 1).
[3 marks]B
Problem Solving & Reasoning
Answer all questions. Show your detailed working.
1.
A line passes through (1, 2) and is parallel to the line 4x - y = 9. Find its equation.
[4 marks]2.
The line y = -2x + 3 is extended to pass through (2, -1). Write the equation of the new line parallel to it.
[4 marks]3.
Explain the process of deriving the equation of a line parallel to y = 5x - 8 and passing through a given point.
[4 marks]4.
If a line is parallel to y = -x + 4 and passes through (0, 0), what is its equation?
[3 marks]5.
Identify the mistake: The equation of a line parallel to y = 2x + 1 passing through (3, 5) is incorrectly written as y = 2x + 8. Correct the mistake and find the proper line equation.
[4 marks]C
Real-world Applications
Solve the following word problems. Show all your working clearly.
1.
A railway track runs parallel to a highway. The highway has the equation y = 3x + 2. Find the equation of the railway track if it passes through (4, 10).
[4 marks]2.
A city planner wants to design a new pedestrian pathway parallel to an existing line y = -0.5x + 5. The pathway must pass through the point (6, 2). What is the equation of this pathway?
[4 marks]D
Challenge & Extension
Attempt these advanced questions. Show your detailed reasoning.
1.
Construct the equation of a line parallel to y = 7x - 3 that passes through the point (-2, 4) using grid paper. Write the final equation.
[4 marks]2.
Given the line 5x + 2y = 10, find the equation of the line parallel to it passing through (1, -2).
[4 marks]3.
For a line parallel to y = -3x + 6 passing through (0, 0), derive its equation and explain each step.
[4 marks]E
Mixed Review
Answer all questions. These test various aspects of finding equations of parallel lines.
1.
What is the slope of any line parallel to y = 4x + 9?
[2 marks]2.
Write the equation of a line parallel to y = -x - 2 and passing through (3, 4).
[3 marks]3.
Identify the error: The line y = 2x + 5 is mistakenly written as y = 2x - 5 as parallel to y = 2x + 3. Correct the error.
[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