SAT Math Multiple Choice Question 639: Answer and Explanation

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Question: 639

9. Which of the following could be the x-intercept and y-intercept of a line that is perpendicular to the line 3x + 6y = 0?

  • A. (-6, 0) and (0, 3)
  • B. (3, 0) and (0, -6)
  • C. (3, 0) and (0, 6)
  • D. (6, 0) and (0, 3)

Correct Answer: B

Explanation:

B

Algebra (linear relationships) MEDIUM

As we discussed in Chapter 7, Lesson 5, a line in the form ax + by = c has a slope of -a/b. Therefore, the line 3x + 6y = 0 has a slope of -3/6 = -1/2. Recall, also, from Chapter 7, Lesson 7, that perpendicular lines have slopes that are opposite reciprocals. Therefore, the line we are looking for must have a slope of 2. You might draw a quick sketch of the xy-plane and plot the points given in each choice to find the line that has a slope of 2, or you could use the slope formula from Chapter 7, Lesson 5: slope = (y2 - y1)/(x2 - x1).

(A) slope = (3 - 0)/(0 - (-6)) = 3/6 = 1/2

(B) slope = (-6 - 0)/(0 - 3) = -6/-3 = 2

(C) slope = (6 - 0)/(0 - 3) = 6/-3 = -2

(D) slope = (3 - 0)/(0 - 6) = 3/-6 = -1/2

The only choice that gives a slope of 2 is (B).

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