The gradient of the straight line joining the points P(5, -7) and Q(-2, -3) is

Analyze the question: We need the gradient (slope) of the line through P(5, -7) and Q(-2, -3).

Concept: The gradient between two points (x₁, y₁) and (x₂, y₂) is

m = (y₂ − y₁) / (x₂ − x₁)

Solution:

Let P(5, -7) = (x₁, y₁) and Q(-2, -3) = (x₂, y₂).

• y₂ − y₁ = -3 − (-7) = -3 + 7 = 4
• x₂ − x₁ = -2 − 5 = -7

m = 4 / (-7) = -4/7

Check by swapping the points: (-7 − (-3)) / (5 − (-2)) = -4 / 7 = -4/7. The result is the same.

Answer: The gradient is -4/7, which matches option C.

Tip: Always subtract the coordinates in the same order on top and bottom. Mixing the order (for example, y₂ − y₁ over x₁ − x₂) flips the sign, which is the most common mistake in gradient questions. A line that goes down as you move right (here, y rises as x falls) must have a negative gradient, so you can quickly check that your sign makes sense.