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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Line k lies in the xy-plane. The x-intercept of line k is a  Question banks Downloads My Bookmarks Reviews Important topics
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Line k lies in the xy-plane. The x-intercept of line k is a [#permalink]
Expert's post 00:00

Question Stats: 58% (01:26) correct 41% (01:34) wrong based on 67 sessions
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 ?

[Reveal] Spoiler:
$$\frac{3}{4}$$

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Question: 12
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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Founder  Joined: 18 Apr 2015
Posts: 13432
Followers: 292

Kudos [?]: 3418  , given: 12318

Re: Line k lies in the xy-plane. The x-intercept of line k is a [#permalink]
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Expert's post
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

$$\frac{9}{2}- 0 / 2 - (- 4 )$$

$$=\frac{9}{2}/6$$$$=\frac{3}{4}$$
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Intern Joined: 22 Aug 2018
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Re: Line k lies in the xy-plane. The x-intercept of line k is a [#permalink]
Can someone explain this in simpler terms? How can one solve this using slope equation?
Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: Line k lies in the xy-plane. The x-intercept of line k is a [#permalink]
Expert's post
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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Sandy
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Re: Line k lies in the xy-plane. The x-intercept of line k is a [#permalink]
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?
Retired Moderator Joined: 07 Jun 2014
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Re: Line k lies in the xy-plane. The x-intercept of line k is a [#permalink]
Expert's post
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 xy-plane. The x-intercept of line k is a [#permalink]
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Expert's post
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 ?

[Reveal] Spoiler:
$$\frac{3}{4}$$

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

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Re: Line k lies in the xy-plane. The x-intercept of line k is a   [#permalink] 05 Jul 2020, 05:02
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