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Quiz Chapter 9: Straight Lines

10 questions ยท Form 3 Mathematics Bab 9: Straight Lines

Question 1 of 10Score: 0

What is the formula for the gradient of a line passing through points (x1, y1) and (x2, y2)?

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. What is the formula for the gradient of a line passing through points (x1, y1) and (x2, y2)?

  1. m = x2 - x1y2 - y1
  2. m = y2 - y1x2 - x1
  3. m = y2 + y1x2 + x1
  4. m = -(x-intercept / y-intercept)
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Answer: B

Gradient m is defined as vertical change divided by horizontal change, which is y2 - y1x2 - x1.

2. What is the equation of the line passing through the origin (0,0) with gradient -4?

  1. y = -4x
  2. y = x - 4
  3. x = -4y
  4. y = -4
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Answer: A

A line passing through the origin has y-intercept c = 0. Substituting m = -4 gives y = -4x.

3. Find the equation of a line parallel to y = 5x - 2 that passes through the point (1, 8).

  1. y = 5x + 3
  2. y = 5x + 8
  3. y = -5x + 13
  4. y = 5x - 3
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Answer: A

Parallel line has gradient m = 5. Substitute (1, 8): 8 = 5(1) + c => c = 3. Equation: y = 5x + 3.

4. Two lines y = 3x + 5 and y = kx - 2 are parallel. What is the value of k?

  1. 3
  2. -3
  3. 13
  4. -13
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Answer: A

Parallel lines have equal gradients (m1 = m2). Since m1 = 3, k must equal 3.

5. The gradient of line AB is -35. What is the ratio of its vertical height to its horizontal distance?

  1. 3 : 5
  2. 5 : 3
  3. -3 : -5
  4. 1 : 1
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Answer: A

Gradient magnitude |m| = vertical distance / horizontal distance = 35, which represents a ratio of 3 : 5.

6. A straight line passes through (0, 6) and has a gradient of 3. What is its equation?

  1. y = 3x + 6
  2. y = 6x + 3
  3. y = 3x - 6
  4. y = -3x + 6
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Answer: A

The point (0, 6) gives y-intercept c = 6. With gradient m = 3, the equation is y = 3x + 6.

7. What is the equation of a vertical line passing through the point (5, -3)?

  1. y = -3
  2. x = 5
  3. y = 5x - 3
  4. x = -3
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Answer: B

All points on a vertical line share the same x-coordinate, so its equation is x = 5.

8. What is the gradient of a vertical line perpendicular to the x-axis?

  1. Undefined
  2. 0
  3. 1
  4. -1
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Answer: A

For a vertical line, x2 - x1 = 0. Division by zero makes the gradient undefined.

9. If a line has an x-intercept of 4 and a y-intercept of 8, what is its gradient?

  1. -2
  2. 2
  3. -0.5
  4. 0.5
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Answer: A

Gradient m = -(y-intercept / x-intercept) = -(84) = -2.

10. Which of the following lines is parallel to y = -2x + 7?

  1. 2y = -4x + 1
  2. y = 2x + 7
  3. y = 0.5x + 3
  4. 2x - y = 5
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Answer: A

Simplify 2y = -4x + 1 to y = -2x + 0.5. Since its gradient is -2, it is parallel to y = -2x + 7.

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