SAT Math Multiple Choice Question 327: Answer and Explanation

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Question: 327

12. Which of the following equations, when graphed on a coordinate plane, will not cross the y-axis?

  • A. 0.5(4x + y) = y - 9
  • B. 2(x + 7) - x = 4(y + 3)
  • C. 0.25(8y + 4x) - 7 = -2(-y + 1)
  • D. 6x - 2(3y + x) = 10 - 3y

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Think conceptually before you start simplifying the equations. The only type of line that does not cross the y-axis is a vertical line (because it runs parallel to the axis). All vertical lines take the form x = a. In other words, a vertical line does not have a y term.

Getting to the Answer: You don't have to completely simplify every equation to answer this question, nor do you need to graph any of the equations. Eliminate equations that will clearly have a y term once simplified. You don't need to worry about the x terms or the constants.

Choice A: Although it may appear that the y terms will cancel, you must first distribute 0.5. The result is 0.5y on the left side of the equation and y on the right, which do not cancel, so eliminate A.

Choice B: No y terms on the left, but 4y on the right, so eliminate B.

Choice (C): 0.25(8y) = 2y on the left, and -2(-y) = 2y on the right, which do indeed cancel, so (C) is correct.

You don't need to waste time checking D-just move on to the next question. (Choice D: -6y on the left and -3y on the right, which do not cancel.)

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