The gradient of the straight line, which passes through (3, 5) and (5, 3) is:

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The question asks for the gradient (slope) of the line through the points (3, 5) and (5, 3). The slope formula is (y2 - y1) / (x2 - x1).

Option A: -2. If we plug in the coordinates as (x1, y1) = (3, 5) and (x2, y2) = (5, 3), we get (3 - 5) / (5 - 3) = (-2) / 2 = -1, not -2. Therefore this is incorrect.

Option B: 0. A slope of 0 would indicate a horizontal line where y does not change with x. Here y changes from 5 to 3 as x goes from 3 to 5, so the slope cannot be 0. This option misinterprets the relationship between x and y for these points.

Option C: -1. This matches the computed value: (3 - 5) / (5 - 3) = -2 / 2 = -1. The line drops by 2 units in y for every 2 units it moves in x, which is a slope of -1. This is the correct calculation.

Option D: 1. A positive slope would mean y increases as x increases. Here, as x increases from 3 to 5, y decreases from 5 to 3, giving a negative slope, so 1 is inconsistent with the actual direction of the line.

MUF0142 Fund. Mathematics Unit 2 - Semester 1, 2025

The gradient of the straight line, which passes through (3, 5) and (5, 3) is:

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