marcodonzelli wrote:

Does the point of intersection of line y = kx + b and line x = ky + b have a negative x-coordinate?

1. k > 0, b > 0

2. k > 1

Yes; the x-coordinate will be negative.

y= kx + b-------1

y= x/k - b/k-----2

Since the 2 equations have inverse slopes, they must represent perpendicular lines.

Take equation 1 first.

If y= 0, x= -b/k; If x= 0, y= b. Joining these 2 points, one gets a line going from -x-coordinate to +y coordinate. Now, if you plot the 2nd equation similarly, you find that when

x = 0, y = -b/k and when y = 0, x = b. On plotting these points it is seen that the 2 lines will intersect in the 3rd quadrant. Thus, x is negative.