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

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Let’s examine the slope calculation step by step using the two given points.
First, recall the slope formula: slope = (y2 − y1) / (x2 − x1).

Option A: "A. - 1". If we compute with the points (3, 5) as (x1, y1) and (5, 3) as (x2, y2), we get slope = (3 − 5) / (5 − 3) = (−2) / 2 = −1. This matches the standard slope result for these coordinates.

Option B: "B. - 2". This would imply a change in y of −4 for a change in x of 2, or a slope of −2, which would require a different pair of points (for example, y changing by −4 while x changes by 2). Here the actual y-change is −2 while the x-change is +2, so −2 is not correct.

Option C: "C. 0". A slope of 0 would mean no vertical change between the points, i.e., y would be the same for both x-values. Since the y-values differ (5 and 3), a horizontal line with slope 0 is inconsistent with this pair of points.

Option D: "D. 1". A positive slope of 1 would require y to increase by the same amount as x increases. Here, as x increases from 3 to 5, y actually decreases from 5 to 3, giving a negative slope. Therefore 1 is incorrect.

In summary, by applying the slope formula to the provided coordinates, the only option that aligns with the resulting value is the negative one, while the others contradict the actual changes in x and y for the given points.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025

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

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