In the xy coordinate plane, line L and K intersect at the point (4,3). Is the product of their slopes negative?
1) The product of the x-intercepts of lines L and K is positive.
2) The product of y-intercepts of lines L and K is negative.
Case 1. The two lines have both positive or both negative x-intercepts. For the point in 1st quadrant, both negative x-intercepts mean the slopes are both +ve. However, both positive x-intercepts can mean positive or negative slopes, and hence not sufficient.
Case 2. The two lines have a positive and a negative x-intercept. The negative intercept definitely means positive slope for the line, but the positive intercept can mean positive or negative slope depending upon whether the point of intersection of the line is greater than or lower than 3. Thus, not sufficient.
Combining, we get only onc scenario. The line that has a -ve y-intercept, has a +ve x-intercept. Therefore the other line needs a +ve x-intercept. A line can have a positive x intercept and a positive y-intercept with +ve slope only.
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