16Hit1600
AlgebraHardLine through a point with the same slope as a given line

Algebra practice question

In the xy-plane, line m has the equation y = −2x + 5. Which equation represents the line that passes through (3, 1) and has the same slope as line m?

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

Answer: A. y = −2x + 7

Slope −2 through (3, 1): 1 = −2(3) + b gives b = 7.

Why the other answers are wrong

B. y = −2x + 1
b = 1 uses the point's y-coordinate as the intercept.
C. y = (1/2)x − 1/2
1/2 is the perpendicular slope, not the same slope.
D. y = −2x + 5
Line m itself does not pass through (3, 1) (it gives −1).

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