Line k lies in the xy-plane. The x-intercept of line k is -4, and line k passes

游客2024-01-12 16

问题 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.

选项

答案 3/4

解析 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 9/2, 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 -(or any equivalent fraction).

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