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.
