We need to find the gradient of the line passing through the points $P(2, -3)$ and $Q(5, 3)$.

GeometryCoordinate GeometryGradientSlope of a Line
2025/6/3

1. Problem Description

We need to find the gradient of the line passing through the points P(2,3)P(2, -3) and Q(5,3)Q(5, 3).

2. Solution Steps

The gradient of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is given by the formula:
m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}
In this case, we have (x1,y1)=(2,3)(x_1, y_1) = (2, -3) and (x2,y2)=(5,3)(x_2, y_2) = (5, 3).
Plugging these values into the formula, we get:
m=3(3)52m = \frac{3 - (-3)}{5 - 2}
m=3+33m = \frac{3 + 3}{3}
m=63m = \frac{6}{3}
m=2m = 2

3. Final Answer

The gradient of the line is

2. Therefore, the answer is C.

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