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Line k lies in the xy-plane. The x-intercept of line k is a
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14 Dec 2015, 07:15
14 Dec 2015, 07:15
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Question Stats:
63% (01:38) correct
36% (01:40) wrong based on 155 sessions
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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 and (2, 9), and (2, 0). What is the slope of line k ?
Give your answer as a fraction.
Give your answer as a fraction.
Show: ::
\(\frac{3}{4}\)
Practice Questions
Question: 12
Page: 153
Difficulty: medium
Question: 12
Page: 153
Difficulty: medium
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Re: Line k lies in the xy-plane. The x-intercept of line k is a
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05 Jul 2020, 05:02
05 Jul 2020, 05:02
5
Carcass wrote:
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 and (2, 9), and (2, 0). What is the slope of line k ?
Give your answer as a fraction.
Give your answer as a fraction.
Show: ::
\(\frac{3}{4}\)
GIVEN: The x-intercept of line k is -4
The y-coordinate is always 0 at any x-intercept.
So, we now know that line K passes through the point (-4, 0)
GIVEN: line k passes through the midpoint of the line segment whose endpoints are and (2, 9), and (2, 0)
The MIDPOINT of a line segment with endpoints (2, 9), and (2, 0) is (2, 4.5)
So, we now know that line K passes through the point (2, 4.5)
What is the slope of line k?
Slope = rise/run
= (4.5 - 0)/(2 - (-4))
= 4.5/6
= 9/12
= 3/4
Answer: 3/4
Cheers,
Brent
General Discussion
Re: Line k lies in the xy-plane. The x-intercept of line k is a
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14 Dec 2015, 07:41
14 Dec 2015, 07:41
3
Expert Reply
Solution
The coordinates of the first point are since the x-coordinate is and (−4, 0), −4 the y-coordinate of every point on the x-axis is 0. For the second point, the mid-point of the line segment is halfway between the endpoints and (2, 9) (2, 0). Thus, the midpoint has x-coordinate 2 and y-coordinate
\(\frac{9}{2}\) the number halfway between 9 and 0. Based on the coordinates (−4, 0) and \((2, \frac{9}{2})\), the slope of line k is
\(\frac{9}{2}- 0 / 2 - (- 4 )\)
\(=\frac{9}{2}/6\)\(=\frac{3}{4}\)
The coordinates of the first point are since the x-coordinate is and (−4, 0), −4 the y-coordinate of every point on the x-axis is 0. For the second point, the mid-point of the line segment is halfway between the endpoints and (2, 9) (2, 0). Thus, the midpoint has x-coordinate 2 and y-coordinate
\(\frac{9}{2}\) the number halfway between 9 and 0. Based on the coordinates (−4, 0) and \((2, \frac{9}{2})\), the slope of line k is
\(\frac{9}{2}- 0 / 2 - (- 4 )\)
\(=\frac{9}{2}/6\)\(=\frac{3}{4}\)
