SAT Math Multiple Choice Question 274: Answer and Explanation

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Question: 274


Line L shown in the graph could be the graph of which equation?

  • A. x + y = -2
  • B. x + y = 0
  • C. x + y - 2 = x
  • D. x + y + 2 = x

Correct Answer: D



Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Horizontal and vertical lines have special forms. A horizontal line has a slope of 0 and an equation that always looks like y = b, where b is a constant. A vertical line has an undefined slope and always looks like x = b.

Getting to the Answer: Line L shown in the graph is horizontal, so you are looking for an equation that once simplified (or written in y = mx + b form) looks like y = b. In other words, all the x-terms must cancel out. In addition, because the line is below the x-axis, b must be a negative number. Check each answer choice to see if it takes on the desired form. Choice A → y = -x - 2, so eliminate it. Choice B → y = -x, so eliminate it. Choice C → y = 2, which is in the correct form, but 2 is positive and the graph would be above the x-axis, so eliminate it. This means (D) must be correct-subtracting x and 2 from both sides of the equation results in y = -2, which could be the equation of line L.

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