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A line is drawn straight up the page, so every point on it has the same input value but many different output values. What is true of this line?
AIts rate of change equals its height
BIts rate of change is 1 by definition
CIts rate of change is zero, so it is flat
DIts rate of change cannot be worked out
Answer & Solution
Correct answer: D. Its rate of change cannot be worked out
1. A rate of change divides the change in output by the change in input.
2. On a line drawn straight up the page, every point shares the same input value.
3. So the change in input between any two points is zero.
4. Dividing by zero has no answer, so this line has no rate of change at all.
5. Option C describes the opposite case, a line drawn flat across the page, where the output never changes.
6. Options A and B invent values for something that cannot be worked out.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_
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