16Hit1600
AlgebraHardLine parallel to a given line

Algebra practice question

Which equation represents the line in the xy-plane that passes through the point (2, 1) and is parallel to the line y = −2x + 7?

  1. A. y = −2x + 5Correct
  2. B. y = −2x + 1
  3. C. y = (1/2)x
  4. D. y = −2x − 3

Answer: A. y = −2x + 5

Parallel lines have the same slope, so the slope is −2. Use the point to find the intercept: 1 = −2(2) + b, so b = 5. The line is y = −2x + 5. Check: −2(2) + 5 = 1.

Why the other answers are wrong

B. y = −2x + 1
The point's y-value was used as the intercept. The intercept is found by substituting the point into y = −2x + b, giving b = 5.
C. y = (1/2)x
1/2 is the negative reciprocal of −2, which would make a PERPENDICULAR line. Parallel lines share the same slope.
D. y = −2x − 3
A sign error in 1 = −4 + b: adding 4 to both sides gives b = 5, not −3.

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