SAT Math Multiple Choice Question 327: Answer and Explanation
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
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.)