P is the point (2,7) and Q is the point (6,3). What is the gradient of PQ?
A. 1
B. -1
C. 0.5
D. -0.5
Correct Answer: B
Explanation
The gradient (slope) of the line passing through two points \(P(x_1, y_1)\) and \(Q(x_2, y_2)\) is given by the formula:
\[
\text{Gradient} = \frac{y_2 - y_1}{x_2 - x_1}
\]
For points \(P(2, 7)\) and \(Q(6, 3)\):
1. Substitute the coordinates into the formula:
\[
\text{Gradient} = \frac{3 - 7}{6 - 2} = \frac{-4}{4} = -1
\]
The gradient of the line \(PQ\) is \(-1\).
The correct answer is B. -1.
