Using y - y₁ = m(x - x₁): Challenge & Extension
Mathematics
Year 9
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on using the equation y - y₁ = m(x - x₁) to find equations of lines, plot graphs, and solve real-world problems. Designed for challenge and extension.
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Full preview • 12 questions
Using y - y₁ = m(x - x₁): Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Given the point (3, 4) and gradient m = 2, write the equation of the line using y - y₁ = m(x - x₁).
[2 marks]2.
Plot the line passing through (1, 2) with a gradient of -1 using the grid. Write its equation.
[3 marks]3.
If a line passes through points (2, 5) and (4, 1), find its gradient and write the equation using y - y₁ = m(x - x₁).
[3 marks]4.
Construct the equation of a line passing through (0, 0) with a gradient of 3. Show the working.
[3 marks]5.
A line passes through (5, 7) and is parallel to the line with equation y - 2 = 4(x - 1). Write the equation of this new line.
[4 marks]6.
Find the equation of the line perpendicular to y - 3 = (1/2)(x - 1) passing through (4, 2).
[4 marks]7.
A line goes through (2, 3) and (5, 11). Calculate its gradient and write the equation in y - y₁ = m(x - x₁) form.
[3 marks]8.
Explain the mistake in the following step when trying to find the equation of a line: "Using point (1, 2) and gradient 0, y - 2 = 0(x - 1)." Is this correct? Why or why not?
[4 marks]9.
Using the points (3, 5) and (7, 5), find the equation of the line. Does this line have a positive, negative, or zero gradient?
[3 marks]10.
A road runs through points (0, 0) and (10, 20). Construct its equation and identify whether it’s increasing or decreasing.
[4 marks]11.
Identify and correct the mistake in this calculation: "Given point (4, 6) and gradient 1/2, the equation is y - 6 = 1/2(x - 4)."
[4 marks]12.
Challenge: Find the equation of a line that passes through (1, 1) and is perpendicular to the line y - 2 = 3(x - 2). Then, plot and confirm on the grid.
[5 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