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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.
Q. Line k lies in the xy-plane. The x-intercept of line k is −4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the slope of line k? Give your answer as a fraction.
Correct answer is '3/4'. Can you explain this answer?
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Directions: Your answer may be an integer, a decimal, or a fraction, ...
You can calculate the slope of a line if you know the coordinates of two points on the line. In this question you are given information about two points on line k, namely,
  • the point at which line k crosses the x-axis has x-coordinate −4;
  • the midpoint of the line segment with endpoints at (2, 9) and (2, 0) is on line k.
The coordinates of the first point are (−4, 0), since the x-coordinate is −4 and the y-coordinate of every point on the x-axis is 0. For the second point, the midpoint of the line segment is halfway between the endpoints (2, 9) and (2, 0). Thus, the midpoint has x-coordinate 2 and y-coordinate 9, the number halfway between 9 and 0. Based on the coordinates (−4, 0) and (2,9/2), the slope of line k is
The correct answer is 3/4 (or any equivalent fraction).
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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.Q. Line k lies in the xy-plane. The x-intercept of line k is −4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the slope of line k? Give your answer as a fraction.Correct answer is '3/4'. Can you explain this answer?
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