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What is the y-intercept? Please explain!

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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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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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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
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Want to do it right the first time.
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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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