SAT Math Multiple Choice Question 384: Answer and Explanation

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Question: 384

9. If line L passes through the points (-4, -8) and (8, 1), which of the following points does line L not pass through?

  • A. (0, -5)
  • B. (4, -1)
  • C. (12, 4)
  • D. (16, 7)

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: The slopes between sets of points that lie on the same line are equal. You can find the slope between points using the slope formula or by looking for patterns.

Getting to the Answer: Before immediately jumping to the slope formula, take a peek at the answer choices—all the x-coordinates of the points are multiples of 4, so looking for a pattern is the quickest way to answer this question. It may help to put all the points in a table (including those given in the question stem), with the x-coordinates arranged from smallest to largest, and then see which point doesn't fit the pattern.

x y
-4-8
0-5
4-1
81
124
167

Notice that all the x-coordinates increase by 4, while most of the y-coordinates increase by 3. For the slope between each pair of points to be equal, the y-coordinate at x = 4 would need to be –2, not –1, so the point given in (B) does not lie on the line.

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