Finding Equations: Problem Solving & Reasoning
Mathematics
GCSE Higher
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on finding the equations of lines, including parallel lines, using algebraic methods. Suitable for GCSE Higher students to develop problem-solving skills.
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Full preview • 15 questions
Finding Equations: Problem Solving & Reasoning
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the key concept below before attempting the questions.
1.
The equation of a straight line in slope-intercept form is y=mx+c, where m is the slope and c is the y-intercept. To find the equation of a line parallel to a given line, use the same slope but a different intercept.
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Find the equation of the line passing through (2, 3) with a slope of 4.
[2 marks]2.
Write the equation of a line parallel to y=2x+1 that passes through the point (5, -1).
[2 marks]3.
Determine the equation of a line with slope -3 passing through (0, 4).
[2 marks]C
Targeted Problems
Answer all questions. Use algebraic methods to find the equations.
1.
A line passes through the points (1, 2) and (3, 6). Find the equation of the line in y=mx+c form.
[3 marks]2.
Find the equation of the line parallel to y=-1/2x+3 that passes through (-2, 5).
[2 marks]3.
Determine the equation of a line with slope 5 that goes through the origin.
[2 marks]4.
A line has equation y=3x-7. Find the equation of a line parallel to it that crosses the y-axis at 4.
[2 marks]5.
Construct the equation of a line passing through (4, -2) with slope 1/2.
[3 marks]D
Real-world Applications
Solve the following contextual problems involving finding equations.
1.
A delivery driver starts at point (0, 0) and drives in a straight line with a constant speed, following the equation y=3x. Write the equation of the driver’s route and describe its meaning.
[3 marks]2.
A railway track runs through points (2, 5) and (6, 13). Find the equation of the track in slope-intercept form.
[3 marks]E
Challenge & Extension
Attempt these challenging questions for extra practice.
1.
Determine the equation of a line parallel to 2x - 3y = 6 that passes through the point (1, -2).
[3 marks]2.
A line has the equation y= -4x + 10. Find the equation of a parallel line passing through (0, 0).
[2 marks]F
Mixed Review & Error Analysis
Answer all questions carefully. Review the common mistakes described.
1.
A student claims that the equation of a line parallel to y=5x+2 passing through (3, 7) is y=5x+10. Identify and correct the mistake.
[3 marks]2.
Calculate the equation of a line with slope 2 passing through (4, 1).
[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.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet