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

Question

BlackTom AI · Accepted Answer

The gradient (slope) formula for a straight line through two points is m = (y2 − y1) / (x2 − x1).

1. Relevant knowledge points and concepts
- Gradient (slope) measures the rate of change of y with respect to x.
- For two points (x1, y1) and (x2, y2), use m = (y2 − y1) / (x2 − x1).
- Order of subtraction must be consistent (same assignment of point 1 and point 2).

2. Complete reasoning process step by step
- Choose (x1, y1) = (3, 5) and (x2, y2) = (5, 3).
- Apply the slope formula directly.

3. Calculations with intermediate steps
- y2 − y1 = 3 − 5 = −2
- x2 − x1 = 5 − 3 = 2
- m = (y2 − y1) / (x2 − x1) = (−2) / 2 = −1

4. Why the correct answer is correct
- The computed slope is −1, which means for every 1 unit increase in x the value of y decreases by 1. This exactly matches option A (−1).

5. Why the other options are incorrect
- B. 0 would mean y is constant (horizontal line); here y changes from 5 to 3 so slope is not 0.
- C. −2 would result if the denominator were 1 (or if we misordered points as (5,3) minus (3,5) for x only), but with x change = 2 the slope is (−2)/2 = −1, not −2.
- D. 1 would require y to increase when x increases; here y decreases from 5 to 3, so slope is negative, not positive 1.

6. Conclusion
- The correct gradient is −1, which corresponds to option A. This matches the provided answer.

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

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