Straight Lines
Overview
Straight lines are the simplest curves in coordinate geometry, yet they carry an enormous amount of information. A single equation can describe every point on a line, predict where two lines cross, and reveal whether lines run parallel or meet at right angles. Mastering these ideas gives you a toolkit that appears in almost every other topic on the 4PM1 paper.
In this topic you will calculate gradients, write equations in several standard forms, and apply the conditions for parallel and perpendicular lines. Every technique translates directly into exam marks, so the worked examples follow the exact method that examiners reward.
Objectives
- Calculate the gradient of a straight line joining two points
- Know and use the forms y = mx + c and y - y1 = m(x - x1) for the equation of a straight line
- Interpret ax + by = c as a straight line
- Determine the condition for two lines to be parallel or perpendicular
Mind map
This topic is mapped out so you can see how the ideas connect.
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
Complete Note Available on the Green Bridge App
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Lesson Evaluation
Congratulations on completing the lesson on Straight Lines. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What is the gradient of the line joining (2, 3) and (6, 11)? A) 1/2 B) 2 C) 4 D) 8 Answer: B
- Which of the following lines is parallel to y = 5x - 3? A) y = -5x + 1 B) y = 5x + 7 C) y = x/5 + 2 D) y = -x/5 + 4 Answer: B
- Two perpendicular lines have gradients m1 and m2. Which equation must hold? A) m1 + m2 = 0 B) m1 = m2 C) m1 x m2 = -1 D) m1 x m2 = 1 Answer: C
- The line 4x + 2y = 10 has gradient: A) 4 B) 2 C) -2 D) -4 Answer: C
- A line passes through (0, 7) with gradient -3. What is its equation? A) y = -3x + 7 B) y = 3x + 7 C) y = -3x - 7 D) y = 7x - 3 Answer: A
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Practice Mock Questions
Want to practice mock questions on Straight Lines? Download the Green Bridge CBT app to access mock questions and full practice assessments for this topic.
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