# 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 3*x* + 6*y* = 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 3*x* + 6*y* = 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 = (*y*_{2} - *y*_{1})/*(x*_{2} - *x*_{1}).

(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).