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AlgebraMediumChecking statements about a linear graph

Algebra practice question

Which of the following statements is true about the graph of y = −(3/4)x + 6 in the xy-plane?

  1. A. For every 4 units the graph moves to the right, it falls 3 units.Correct
  2. B. The graph crosses the x-axis at x = 6.
  3. C. The graph passes through the point (4, 2).
  4. D. For every 3 units the graph moves to the right, it rises 4 units.

Answer: A. For every 4 units the graph moves to the right, it falls 3 units.

Slope −3/4 means a fall of 3 for each 4 to the right. The x-intercept is 8, and at x = 4 the value is 3.

Why the other answers are wrong

B. The graph crosses the x-axis at x = 6.
6 is the y-intercept; the x-intercept is 8.
C. The graph passes through the point (4, 2).
At x = 4, y = −3 + 6 = 3, not 2.
D. For every 3 units the graph moves to the right, it rises 4 units.
The graph falls, and the ratio is 3 down per 4 across, not 4 up per 3.

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