SAT Math Multiple Choice Question 99: Answer and Explanation

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Question: 99


The graph of f(x) is shown above in the xy-plane. The points (0, 3), (5b, b), and (10b, -b) are on the line described by f(x). If b is a positive constant, what are the coordinates of point C ?

  • A. (5, 1)
  • B. (10, -1)
  • C. (15, -0.5)
  • D. (20, -2)

Correct Answer: B


BRight away, (A) can be eliminated, since point C has a negative y-coordinate. Given any two points, the slope of the line can be determined using the equation . Use this formula to find the value of b by setting the slope of equal to the slope of Use points (0, 3) and (5b, b) in the left side of the equation and points (5b, b) and (10b, -b) in the right side of the equation to get . Simplify both sides of the equation to get , or . Cross-multiply to get 5(3 - b) = 10b. Divide both sides by 5 get 3 - b = 2b, then 3 = 3b, and finally b = 1. Plug in b =1 for point C to get [10(1), - (1)], or (10, -1). Therefore, the correct answer is (B).

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