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AlgebraHardQuadrant a line does not pass through

Algebra practice question

In the xy-plane, a line passes through the points (3, −2) and (−1, 6). Which quadrant does the line NOT pass through?

  1. A. Quadrant IIICorrect
  2. B. Quadrant I
  3. C. Quadrant II
  4. D. Quadrant IV

Answer: A. Quadrant III

Slope = (6 − (−2))/(−1 − 3) = −2, so y = −2x + 4. It has a positive y-intercept and falls to the right, passing through quadrants II, I, and IV but never III (where x < 0 and y < 0).

Why the other answers are wrong

B. Quadrant I
Between x = 0 and x = 2 the line is in quadrant I.
C. Quadrant II
For x < 0 the line is above the axis, in quadrant II.
D. Quadrant IV
For x > 2 the line is below the axis, in quadrant IV.

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