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-intercepts of lines l and k is positive.
2) The product of the y-intercepts of lines l and k is negative.
Please explain your answer
This question has a great takeaway - something I am sure you know intuitively but you may not think of it while doing this question because it is seldom written out:
The slope of a line is -(y intercept)/(x intercept)
Above, sreehari uses this concept to solve the question very efficiently.
If you are wondering why it is so, think what 'intercept' represents...
The point of x intercept is (x, 0) (where y co-ordinate is 0)
The point of y intercept is (0, y) (where x co-ordinate is 0)
So slope = (y - 0)/(0 - x) = -y/x
Thanks I realized it only now; slope =-(y intercept)/(x intercept)