SAT Math Multiple Choice Question 457: Answer and Explanation

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Question: 457

7. If the graph of y = mx + b passes through quadrants I, III, and IV on a coordinate plane, which of the following must be true about m and b?

  • A. m < 0, b < 0
  • B. m < 0, b > 0
  • C. m > 0, b < 0
  • D. m > 0, b > 0

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: Draw a quick sketch of the line described and compare it to the answer choices. Don't forget, the quadrants start with I in the upper right corner and move counterclockwise.

Getting to the Answer: A sample sketch follows:

Notice that the line is increasing, so the slope is positive (m > 0). This means you can eliminate A and B. The line crosses the y-axis below the origin, so b is negative (b < 0), which means (C) is correct.

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