16Hit1600
AlgebraHardEquation of a line through two points

Algebra practice question

Which equation represents the line in the xy-plane that passes through (−1, 1) and (3, 7)?

  1. A. y = (3/2)x + 5/2Correct
  2. B. y = (3/2)x + 1
  3. C. y = (2/3)x + 5/3
  4. D. y = 6x + 7

Answer: A. y = (3/2)x + 5/2

Slope (7 − 1)/(3 − (−1)) = 3/2. Then 1 = (3/2)(−1) + b gives b = 5/2.

Why the other answers are wrong

B. y = (3/2)x + 1
b = 1 uses the point's y-coordinate as the intercept; check x = −1: −1/2 ≠ 1.
C. y = (2/3)x + 5/3
2/3 is the reciprocal slope.
D. y = 6x + 7
6 is the rise alone, not divided by the run of 4.

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