In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p),\)

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p),\)

by Vincen » Tue Aug 18, 2020 8:10 am

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In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p),\) what is the value of \(p ?\)

A. -2
B. 0
C. 1/2
D. 1
E. 2

Answer: D

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Tue Aug 18, 2020 8:10 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p)

by Scott@TargetTestPrep » Sat Aug 22, 2020 8:52 am

Vincen wrote: ↑
Tue Aug 18, 2020 8:10 am
In the rectangular coordinate system, if the line \(x = 2y + 5\) passes through points \((m,n)\) and \((m + 2,n + p),\) what is the value of \(p ?\)

A. -2
B. 0
C. 1/2
D. 1
E. 2

Answer: D

Solution:

The equation of the given line in slope-intercept form is:

2y + 5 = x

2y = x - 5

y = (1/2)x - 5/2

We see that the given line has a slope of 1/2. We can use the slope formula and substitute the “values” of the points (m,n) and (m + 2, n + p) into it: :

(n + p - n) / (m + 2 - m) = 1/2

p/2 = 1/2

p = 1

Answer: D

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