The quadrants of the
xy−plane are defined as follows: Quadrant I is above the
x−axis and to the right of the
y−axis; Quadrant II is above the x-axis and to the left of the y-axis; Quadrant III is below the
x−axis and to the left of the y-axis; and Quadrant IV is below the x-axis and to the right of the
y−axis. It is possible for line
l to pass through Quadrants II, III, and IV, but not Quadrant I, only if line
l has negative
x−and
y−intercepts. This implies that line l has a negative slope, since between the negative x-intercept and the negative
y−intercept the value of
x increases (from negative to zero) and the value of
y decreases (from zero to negative); so the quotient of the change in y over the change in
x, that is, the slope of line
l, must be negative.
Choice A is incorrect because a line with an undefined slope is a vertical line, and if a vertical line passes through Quadrant IV, it must pass through Quadrant I as well. Choice B is incorrect because a line with a slope of zero is a horizontal line and, if a horizontal line passes through Quadrant II, it must pass through Quadrant I as well. Choice C is incorrect because if a line with a positive slope passes through Quadrant IV, it must pass through Quadrant I as well.