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Line k lies in the xyplane. The xintercept of line k is a [#permalink]
14 Dec 2015, 07:15
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Line k lies in the xyplane. The xintercept 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. Practice Questions Question: 12 Page: 153 Difficulty: medium
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Re: Line k lies in the xyplane. The xintercept of line k is a [#permalink]
14 Dec 2015, 07:41
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SolutionThe coordinates of the first point are since the xcoordinate is and (−4, 0), −4 the ycoordinate of every point on the xaxis is 0. For the second point, the midpoint of the line segment is halfway between the endpoints and (2, 9) (2, 0). Thus, the midpoint has xcoordinate 2 and ycoordinate \(\frac{9}{2}\) the number halfway between 9 and 0. Based on the coordinates (−4, 0) and \((2, \frac{9}{2})\), the slope of line k is \(\frac{9}{2} 0 / 2  ( 4 )\) \(=\frac{9}{2}/6\)\(=\frac{3}{4}\)
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Re: Line k lies in the xyplane. The xintercept of line k is a [#permalink]
13 Sep 2018, 09:36
Can someone explain this in simpler terms? How can one solve this using slope equation?



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Re: Line k lies in the xyplane. The xintercept of line k is a [#permalink]
14 Sep 2018, 15:53
rajlal wrote: Can someone explain this in simpler terms? How can one solve this using slope equation? It is better not to solve this by using a standard line equation. The reason being a line equation is represented as: \(y=mx+c\) where m is the slope and c is the y intercept. Here we have the x intercept. Now we can rewrite the equation \(y=mx+c\) as \(x=\frac{1}{m}y+k\) where \(k=\frac{c}{m}\). This value is given n the question as 4.
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Re: Line k lies in the xyplane. The xintercept of line k is a [#permalink]
15 Sep 2018, 01:40
sandy wrote: rajlal wrote: Can someone explain this in simpler terms? How can one solve this using slope equation? It is better not to solve this by using a standard line equation. The reason being a line equation is represented as: \(y=mx+c\) where m is the slope and c is the y intercept. Here we have the x intercept. Now we can rewrite the equation \(y=mx+c\) as \(x=\frac{1}{m}y+k\) where \(k=\frac{c}{m}\). This value is given n the question as 4. I am sorry, but I don't understand your approach! How does this match the answer?



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Re: Line k lies in the xyplane. The xintercept of line k is a [#permalink]
15 Sep 2018, 12:06
rajlal wrote: I am sorry, but I don't understand your approach! How does this match the answer? For you to solve the line using line equation \(y=mx+c\) you need to find the values of both m and c. You can solve them by putting points (4, 0) and the mid point of (2, 9), and (2, 0) into \(y=mx+c\). However that would make it unecessarily long. You can directly solve for the slope using the metod presented in the solution post by Carcass.
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Re: Line k lies in the xyplane. The xintercept of line k is a [#permalink]
05 Jul 2020, 05:02
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Carcass wrote: Line k lies in the xyplane. The xintercept 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. GIVEN: The xintercept of line k is 4The ycoordinate is always 0 at any xintercept. 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= 3/4Answer: 3/4 Cheers, Brent
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Re: Line k lies in the xyplane. The xintercept of line k is a
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