swerve wrote:In the xy coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?
1) The product of the x-intersects of lines L and K is positive.
2) The product of the y-intersects of lines L and K is negative.
Statement 1: The product of the x-intercepts of line L and K is positive.
K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive:
K has a positive x-intercept, L has a positive x-intercept, the product of the slopes is negative:
INSUFFICIENT.
Statement 2: The product of the y-intercepts of line L and k is negative.
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is negative:
K has a negative y-intercept, L has a positive y-intercept, the product of the slopes is positive:
INSUFFICIENT.
Statements 1 and 2 combined:
Statement 1 requires that both x-intercepts be negative or that both x-intercepts be positive (so that their product is positive).
If both x-intercepts are negative, then both y-intercepts must be positive, violating statement 2:
Thus, both x-intercepts must be positive.
Statement 2 requires that one of the y-intercepts be positive, the other negative.
A positive x-intercept and a positive y-intercept yields a negative slope.
A positive x-intercept and a negative y-intercept yields a positive slope.
See below:
Thus, the product of the slopes must be negative.
SUFFICIENT.
The correct answer is
C.
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