y-intercept of line l?

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Feb 10, 2013 6:49 pm

Hello,

This is from one of the practise exams:

In the xy-plane, what is the y-intercept of line l?

1) The slope of line l is 3 times its y-intercept
2) The x-intercept of line l is -1/3

Answer: E

Can you please assist with this? Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Problem Solving | Sun Feb 10, 2013 6:49 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Feb 10, 2013 9:51 pm

gmattesttaker2 wrote:In the xy-plane, what is the y-intercept of line l?

1) The slope of line l is 3 times its y-intercept
2) The x-intercept of line l is -1/3

If the slope and y-intercept of a line in xy plane are m and c respectively, then the line can be represented by the equation y = mx + c and the x=intercept of the line will be -c/m

Statement 1: m = 3c ---> Not sufficient

Statement 2: -c/m = -1/3 ---> m = 3c ---> Not sufficient

1 & 2 Together: We have no new information ---> Not sufficient

The correct answer is E.

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vishugogo: Master | Next Rank: 500 Posts; Posts: 131; Joined: Tue Aug 30, 2011 4:50 amFollowed by: 6 members; Location: India; Thanked: 28 times

by vishugogo » Mon Feb 11, 2013 6:08 am

how is the x-intercept = -c/m ??

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Feb 11, 2013 6:51 am

gmattesttaker2 wrote:
In the xy-plane, what is the y-intercept of line l?

1) The slope of line l is 3 times its y-intercept
2) The x-intercept of line l is -1/3

If you haven't memorized formulas for x-intercepts (I haven't), you don't need them here. We know that the general equation of a line is y = mx + b, where m is the slope, and b is the y-intercept. We need to find the value of b.

Neither statement is sufficient alone. From Statement 2, we know that (-1/3, 0) is a point on our line, so if we plug x = -1/3 and y = 0 into our equation, what we get will be true:

y = mx + b
0 = m(-1/3) + b
m = 3b

So if Statement 2 is true, then it must always be true that the slope is 3 times the y-intercept. That is, Statement 1 gives us no new information at all, and the answer is E.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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