Coordinate Geometry

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swerve: Legendary Member; Posts: 2579; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon Aug 24, 2020 10:36 am

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In the coordinate system above, which of the following could be the equation of the line $p$?

A. $5x + 12y = 30$
B. $12x + 5y = 30$
C. $5x – 12y = 30$
D. $12x – 5y = 30$
E. $5x + 12y = –30$

The OA is A

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Mon Aug 24, 2020 10:36 am

sjain296: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Fri Jun 28, 2019 9:57 pm

Re: Coordinate Geometry

by sjain296 » Tue Aug 25, 2020 1:38 am

From the diagram, we can say that slope of the line should be -Ve

therefore, option C and D are out.

From the diagram, it's also clear that Y-intercept is greater than 2 and lower than 3.

Therefore, if we take x = 0
then, E is out as it's -ve intercept.
B is out as it is more than 3.

So we are left with A.

Therefore, A is the answer.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8210; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Coordinate Geometry

by Scott@TargetTestPrep » Sat Sep 05, 2020 12:22 pm

swerve wrote: ↑
Mon Aug 24, 2020 10:36 am
GMAT_PS_Magoosh_212.png

In the coordinate system above, which of the following could be the equation of the line $p$?

A. $5x + 12y = 30$
B. $12x + 5y = 30$
C. $5x – 12y = 30$
D. $12x – 5y = 30$
E. $5x + 12y = –30$

The OA is A

Solution:

We see that the x-intercept of the line is 6 and the y-intercept is 2.5. We can use the two-intercept form of the line: x/a + y/b = 1 (where a is the x-intercept and b is the y-intercept) to set up an equation for the line. Therefore, the two-intercept form of line p is:

x/6 + y/2.5 = 1

Multiplying both sides by 30, we have:

5x + 12y = 30

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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