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Four charges are written as rules. Which one never reaches zero, so its line never crosses the horizontal axis?
AA rule of the form y = 4x - 12
BA rule of the form y = 0.5x + 3
CA rule of the form y = 30 - 2x
DA flat rule of the form y = 18
Answer & Solution
Correct answer: D. A flat rule of the form y = 18
1. A line crosses the horizontal axis at the input value that makes the output zero.
2. For y = 4x - 12, setting the output to zero gives x = 3, so it does cross.
3. For y = 0.5x + 3, setting the output to zero gives x = -6, so it does cross.
4. For y = 30 - 2x, setting the output to zero gives x = 15, so it does cross.
5. For y = 18 the output is 18 for every input, so it is never zero and the line stays 18 units above the axis.
6. A flat rule with a value other than zero is the only kind of straight line that misses the horizontal axis.
7. Options A, B and C all have a rate of change that is not zero, so each one must cross the axis somewhere.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 4 "Linear Functions", section 4.1 Linear Functions_
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