10 questions ยท Form 3 Mathematics Bab 9: Straight Lines
What is the formula for the gradient of a line passing through points (x1, y1) and (x2, y2)?
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)?
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?
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).
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?
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?
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?
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)?
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?
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?
Answer: A
Gradient m = -(y-intercept / x-intercept) = -(84) = -2.
10. Which of the following lines is parallel to y = -2x + 7?
Answer: A
Simplify 2y = -4x + 1 to y = -2x + 0.5. Since its gradient is -2, it is parallel to y = -2x + 7.