SAT Math Multiple Choice Question 793: Answer and Explanation

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Question: 793


If the equation of line A shown on the graph is given by y = mx + b, and the equation of line B is given by y = k(mx + b), what is the value of k?

  • A.
  • B.
  • C. 6
  • D. 9

Correct Answer: B



Difficulty: Hard

Category: Heart of Algebra / Linear Equations

Strategic Advice: The equation of line B is given as a multiple of line A, so start by finding the equation of each line using its slope and y-intercept. Then compare the equations.

Getting to the Answer: First, determine the equation of line A. Remember that slope is equal to rise over run, so count the change in y and the change in x from one point on the line to the next. The slope is or just 3. Next, find the y-intercept: 9. Now, find the equation of line B: The slope is, and the y-intercept is 2. So, the equations are: Line A: y = 3x + 9 and Line B:. Notice that the numbers in the equation of line A are larger, so k must be a fraction, which means you can eliminate C and D. To choose between A and (B), multiply the number by the equation of line A to see if it matches the equation of line B. Because (the equation of line B),. Therefore, (B) is correct.

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