AlgebraMediumParallel line with a given intercept
Algebra practice question
In the xy-plane, line m is parallel to the line 3x − y = 4 and has a y-intercept of −2. Which equation represents line m?
- A. y = 3x − 2Correct
- B. y = −3x − 2
- C. y = (1/3)x − 2
- D. y = 3x + 4
Answer: A. y = 3x − 2
3x − y = 4 rearranges to y = 3x − 4, slope 3. A parallel line has the same slope, and with intercept −2 it is y = 3x − 2.
Why the other answers are wrong
- B. y = −3x − 2
- −3 is the wrong sign for the slope; the given line has slope 3.
- C. y = (1/3)x − 2
- 1/3 would be the reciprocal; parallel lines share the slope exactly.
- D. y = 3x + 4
- y = 3x + 4 has the right slope but the wrong intercept (and it isn't the given line either, which is y = 3x − 4).
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