Find the slope through (2, 4) and (5, 10).
Incorrect answer: −2
Changing the subtraction order in only one part changes the sign incorrectly. Reverse both numerator and denominator together if you reverse the point order.
Reversing just one subtraction in slope
Both coordinate differences must use the same point order. A line going down as x increases has negative slope.
The correction
2
(10 − 4)/(5 − 2) = 6/3.
- Choose two distinct points and label their coordinates consistently.
- Subtract y-values in the same point order as x-values.
- Divide and interpret the sign and units. A zero denominator indicates a vertical line with undefined slope.
Try the reasoning in another example
Find the slope through (0, 5) and (2, 1).
- Change in y is 1 − 5 = −4.
- Change in x is 2; divide −4 by 2.
Answer: −2
Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.
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