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. 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.
3. 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.
4. Find the point of intersection between lines y = x + 2 and y = -x + 6.
Answer: A
Set equations equal: x + 2 = -x + 6 => 2x = 4 => x = 2. Then y = 2 + 2 = 4. The intersection point is (2, 4).
5. What is the gradient of the line 3x + 4y = 12?
Answer: B
Rearrange 3x + 4y = 12 to y = mx + c: 4y = -3x + 12 => y = (-34)x + 3. Thus, gradient m = -34.
6. Which point lies on the straight line y = 2x - 3?
Answer: B
Substitute x = 2 into y = 2(2) - 3 = 4 - 3 = 1. The point (2, 1) satisfies the equation.
7. 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.
8. 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.
9. 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.
10. 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.