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# In the xy-plane, Line K and K pass through point (1,1), K's

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Manager
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In the xy-plane, Line K and K pass through point (1,1), K's [#permalink]  22 Jul 2009, 11:47
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In the xy-plane, Line K and K pass through point (1,1), K's Y-intercept is greater than L's Y-intercept?
1). K's slope is less than that of L
2). L's slope is negative.
Senior Manager
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Re: INTERCEPT SLOPE DS [#permalink]  22 Jul 2009, 12:05
vcbabu wrote:
In the xy-plane, Line K and K pass through point (1,1), K's Y-intercept is greater than L's Y-intercept?
1). K's slope is less than that of L
2). L's slope is negative.

Ans is A

can do it by 2 methods.
1) eqn y = mx + c

if y and x are same at a point, then lesser the m, greater the C.

2) imagine the 2 lines, and assume L to be anything, say x=y
as you reduce the slope of K, C increases, and vice versa.
Director
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Re: INTERCEPT SLOPE DS [#permalink]  22 Jul 2009, 12:05
C

1)
a) If K's slope is negative and L's slope is negative then K's y-intercept is less than that of L.
b) If K's slope is positive and L's slope is positive then K's y-intercept is greater than that of L.

INSUFF

2) We don't know about other line's slope.

INSUFF

Combining,
L's slope is negative and K's slope is less than that of L. This means K's slope is also negative.
=> y-intercept of K is less than that of L.
Manager
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Re: INTERCEPT SLOPE DS [#permalink]  25 Jul 2009, 06:46
1)
a) If K's slope is negative and L's slope is negative then K's y-intercept is less than that of L.
b[/color]) If K's slope is positive and L's slope is positive then K's y-intercept is greater than that of L.

INSUFF

2) We don't know about other line's slope.

INSUFF

Combining,
L's slope is negative and K's slope is less than that of L. This means K's slope is also negative.
=> y-intercept of K is less than that of L.

Director
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Re: INTERCEPT SLOPE DS [#permalink]  25 Jul 2009, 08:36
Best way to visualize is to draw the lines.

Negative slope means the line rises as we go from right to left i.e. the highest point is on the left side of Y-axis.

Positive slope means the line rises as we go from left to right. i.e the highest point is on the right side of Y-axis.

Also, lesser slope means the 'rise' is less and viceversa. Hope you got the point.
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Re: INTERCEPT SLOPE DS [#permalink]  25 Jul 2009, 13:22
For me it is clearly A.

1) eqn y = mx + c
if y and x are same at a point, then lesser the m, greater the C.
a) If K's slope is negative and L's slope is negative then K's y-intercept is GREATER than that of L.
b) If K's slope is positive and L's slope is positive then K's y-intercept is GREATER than that of L.

Draw the following graphs:
2x - 1 (slope 2, y-intercept -1)
4x - 3 (slope 4, y-intercept -3)
The less the scope, the major is the interception

-2x + 3 (slope -2, y-intercept 3)
-4x + 5 (slope -2, y-intercept 5)
The less the scope, the major is the interception
SUFFICIENT

2) ok, but what about K? Without reference, without comparison.
NOT SUFFICIENT

PS.: If you like the explanation, and mainly, if it is right, consider a kudo! I am trying to access the GMATClub tests!!!
Director
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Re: INTERCEPT SLOPE DS [#permalink]  26 Jul 2009, 02:59

My mistake was:
For negative slope I assumed that the rise is higher if the slope is higher ( just like for positive slopes )

However, if slopes are negative then the rise is higher if the slope is lesser!!!
See figure by mrsmarthi in:
quick-way-to-graph-inequalities-76255.html?highlight=mrsmarthi
Re: INTERCEPT SLOPE DS   [#permalink] 26 Jul 2009, 02:59
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