The Equation Of A Straight Line
Overview
A straight line is the simplest graph there is, and yet it underlies an enormous amount of mathematics. Its entire behaviour is captured by two numbers: a gradient that fixes its steepness and an intercept that fixes its position. Master the equation of a line and coordinate geometry opens up.
In this lesson you will use the two standard forms, \(y=mx+c\) and \(y-y_1=m(x-x_1)\), to find the equation of a line from a gradient and a point, or from two points. These are the everyday tools of the coordinate geometry section.
Objectives
- Use the equation of a straight line in the forms y = mx + c and y - y1 = m(x - x1).
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Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on The Equation Of A Straight Line. 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.
- In y = mx + c, the letter c represents the: A. gradient B. y-intercept C. x-intercept D. midpoint Answer: B
- The equation of the line with gradient 2 through (3, 4) is: A. y = 2x - 2 B. y = 2x + 2 C. y = 2x - 10 D. y = 2x + 4 Answer: A
- The gradient of the line through (1, 2) and (4, 11) is: A. 2 B. 3 C. 9 D. 1/3 Answer: B
- The equation of the line through (1, 2) and (4, 11) is: A. y = 3x - 1 B. y = 3x + 1 C. y = x + 1 D. y = 3x - 7 Answer: A
- Which is the point-gradient form of a line? A. y = mx + c B. y - y1 = m(x - x1) C. y = m + cx D. x = my + c Answer: B
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