10 questions ยท Form 2 Mathematics Bab 10: Gradient of a Straight Line
A line passes through (3, k) and (7, 10) with a gradient of 2. Find the value of k.
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. A line passes through (3, k) and (7, 10) with a gradient of 2. Find the value of k.
Answer: A
10 - k7 - 3 = 2 => 10 - k4 = 2 => 10 - k = 8 => k = 2.
2. Find the gradient of the line passing through (-4, -2) and (2, 1).
Answer: A
m = 1 - (-2)2 - (-4) = 1 + 22 + 4 = 36 = 0.5.
3. What is the formula to calculate the gradient of a line passing through (x1, y1) and (x2, y2)?
Answer: A
Gradient m is defined as the vertical change divided by the horizontal change: y2 - y1x2 - x1.
4. If a line has an x-intercept of 4 and a y-intercept of 8, what is its gradient?
Answer: A
m = -(y-intercept / x-intercept) = -(84) = -2.
5. A straight line has an x-intercept of -3 and a y-intercept of -6. Calculate its gradient.
Answer: A
m = -(y-intercept / x-intercept) = -(-6 / -3) = -(2) = -2.
6. Find the y-intercept of a line with gradient -3 that passes through the x-intercept 2.
Answer: A
m = -(y-intercept / x-intercept) => -3 = -(y-intercept / 2) => y-intercept = 6.
7. The gradient of line AB is 34. If point A is (-1, 2) and point B is (3, y), find y.
Answer: A
y - 23 - (-1) = 34 => y - 24 = 34 => y - 2 = 3 => y = 5.
8. What is the gradient of any horizontal line?
Answer: A
A horizontal line has zero vertical change (y2 - y1 = 0), so its gradient is 0.
9. If the gradient of a line is -1.5 and its y-intercept is 9, find its x-intercept.
Answer: A
-1.5 = -(9x-intercept) => x-intercept = 91.5 = 6.
10. Points C(2, 7) and D(2, -3) lie on the same straight line. The gradient of line CD is:
Answer: A
x-coordinates are identical (x = 2), forming a vertical line. Thus, the gradient is undefined.