Same Gradient: Challenge & Extension

Mathematics
Grade 6
16 questions
~32 mins
1 views0 downloads

About This Worksheet

A challenging worksheet exploring lines with the same gradient, including practice, reasoning, real-world applications, and extension problems for Grade 6 students.

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Same Gradient: Challenge & Extension

Subject: MathematicsGrade: Grade 6
Name:
Date:
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Untitled Worksheet

Grade Grade 6
A

Fluency & Practice

Solve the following questions to practice your understanding of lines with the same gradient.
1.
Calculate the gradient of the line passing through points (2, 3) and (5, 9).
[2 marks]
2.
Find the equation of the line with gradient 3 passing through point (4, 7).
[3 marks]
3.
Determine if the lines passing through (1, 2) and (4, 8), and (0, 0) and (3, 6) are parallel.
[2 marks]
4.
Construct a line with a gradient of -2 passing through the point (3, 5).
[3 marks]
B

Problem Solving & Reasoning

Solve these multi-step problems involving lines with the same gradient and explain your reasoning.
1.
Line A has the equation y=4x+1. Find the equation of a line parallel to it passing through the point (2, 5).
[3 marks]
2.
Two lines are given: y=2x+3 and y=-1/2x+4. Are these lines parallel? Justify your answer.
[3 marks]
3.
A line passes through (0, 2) and is parallel to the line y=5x-1. Find its equation.
[3 marks]
4.
Explain why two lines with the same gradient but different y-intercepts are parallel.
[2 marks]
C

Real-world Applications

Apply your understanding to these real-world scenarios involving parallel lines and gradients.
1.
A railway track runs through two stations, following the line y=2x+3. A new track is to be built parallel to the existing one, passing through point (4, 11). Write its equation.
[3 marks]
2.
A biker travels along a path with the equation y= -1/3x + 4. A new bike lane is to be constructed parallel to this path, passing through (3, 3). Find its equation.
[3 marks]
D

Challenge & Extension

Tackle these advanced problems involving lines with the same gradient, including tricky scenarios and proofs.
1.
Prove algebraically that two lines y=3x+2 and y=3x-5 are parallel. Explain your reasoning.
[4 marks]
2.
Construct a pair of lines on the grid that are parallel with gradient 1/2, passing through points (2, 3) and (4, 5).
[4 marks]
E

Mixed Review

Answer these questions to review your understanding of lines with the same gradient.
1.
Find the gradient of the line passing through (1, 4) and (3, 8).
[2 marks]
2.
Construct a line with gradient -3 passing through (0, 5).
[3 marks]
F

Error Analysis

Identify and correct the mistakes in the following student reasoning.
1.
A student claims lines y=4x+1 and y=4x-3 are not parallel because they intersect at (0,1). Is this correct? Explain and correct if necessary.
[3 marks]
2.
A student finds the gradient of a line passing through (2, 3) and (4, 7) as 3. Is this correct? If not, what is the correct gradient?
[2 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