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x-intercept and slopes

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x-intercept and slopes

by apex231 » Sun Dec 11, 2011 6:43 pm
In the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive?

(1) The slope of line k is -5.
(2) r> 0
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by Anurag@Gurome » Sun Dec 11, 2011 7:46 pm
apex231 wrote:In the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive?

(1) The slope of line k is -5.
(2) r> 0

y = mx + b , where m is the slope
x intercept of the line is at (x,0) so 0 = mx + b
x = -b/m, find if -b/m is positive or not.

(1) m = -5, but there is not info on b.
r = (-5)(-5) + b
r = 25 + b
b = r - 25, but we don't know r is so we cannot find whether -b/m is positive as -b/m = (25 - r)/-5; NOT sufficient.

(2) r > 0
r = -5m + b
-5m + b > 0
b > 5m
5m is negative as we know that the slope is negative. So we cannot find whether -b/m is positive or not; NOT sufficient.

Combining (1) and (2), r = 25 + b
25 + b > 0
b > -25, which can be positive or negative; NOT sufficient.

The correct answer is E.
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