What is the y-intercept? Please explain!

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gmatpup: Senior | Next Rank: 100 Posts; Posts: 88; Joined: Sat Oct 15, 2011 6:38 pmFollowed by: 1 member; Thanked: 1 times

by gmatpup » Fri Dec 23, 2011 6:32 pm

Please explain how to arrive at the answer. Thank you!!

In the xy-plane, line k has a positive slope and x-intercept of 4. If the area of the triangle formed by line k and the two axes is 12, what is the y-intercept of line k?

A. -6
B. -4
C. -3
D. 3
E. 6

Answer is A

I thought the answer was E.. please help me understand. Thanks again!

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Source: Beat The GMAT — Problem Solving | Fri Dec 23, 2011 6:32 pm

chieftang: Master | Next Rank: 500 Posts; Posts: 218; Joined: Wed Nov 23, 2011 8:05 pmFollowed by: 4 members; Thanked: 26 times

by chieftang » Fri Dec 23, 2011 6:37 pm

It's A. The line has a positive slope, i.e. delta(y)/delta(x) > 0. So if the x intercept is 4, then y intercept must be < 0. 1/2*4*h=12 so h=6. But, again, since the line has positive slope, the y intercept must be -6.

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Fri Dec 23, 2011 7:55 pm

gmatpup wrote:Please explain how to arrive at the answer. Thank you!!

In the xy-plane, line k has a positive slope and x-intercept of 4. If the area of the triangle formed by line k and the two axes is 12, what is the y-intercept of line k?

A. -6
B. -4
C. -3
D. 3
E. 6

Answer is A

I thought the answer was E.. please help me understand. Thanks again!

if you imagine the line equation as forming a triangle with co-ordinate axis.
Then x-intercept say a will be your base and y-intercept b will be your height.
so mod(1/2 * a * b) = 12
=> |1/2 * 4 * b| = 12 (a = x-intercept = 4 from question)
=> b = +6 or -6

but line equation if we know intercepts is x/a + y/b = 1
since we need to have slope as +ve we need to have -ve b as we know a is +ve

so should be A

Just started my preparation

Want to do it right the first time.

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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 » Fri Dec 23, 2011 8:11 pm

gmatpup wrote:Please explain how to arrive at the answer. Thank you!!

In the xy-plane, line k has a positive slope and x-intercept of 4. If the area of the triangle formed by line k and the two axes is 12, what is the y-intercept of line k?

A. -6
B. -4
C. -3
D. 3
E. 6

Answer is A

I thought the answer was E.. please help me understand. Thanks again!

Positive slope and positive x-intercept implies that y-intercept should be negative.
Area of triangle = (1/2) * (value of x-intercept) * (value of y-intercept) = (1/2) * 4 * |y| = 12
|y| = 6, but y-intercept should be negative, so y = -6

The correct answer is A.

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