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One line has a rate of change of 4. A second line crosses it at a right angle. What is the rate of change of the second line?
AMinus 0.25
BMinus 4.00
CPlus 0.25
DPlus 4.00
Answer & Solution
Correct answer: A. Minus 0.25
1. Lines that cross at a right angle have rates of change that are negative reciprocals of one another.
2. Find the reciprocal first by dividing 1 by 4, which gives 0.25.
3. Then change the sign, which gives minus 0.25.
4. Check the pair by multiplying: 4 times minus 0.25 is minus 1, as it should be.
5. Option C keeps the reciprocal but forgets the sign change, so those two lines would never meet at a right angle.
6. Option B changes the sign but never takes the reciprocal.
7. Option D repeats the first rate, which would give a parallel line instead.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_
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