A positive slope is a line where changes in the x and y coordinates always have the same sign and move upwards from left to right.   A negative slope is a line where the changes in the x and y coordinates always have a different sign and move downwards from left to right.   The undefined slope is the slope of a vertical line. For such a line, the x-coordinates remain constant regardless of the change in the y-coordinates. Vertical lines do not run left or right. Instead, they rise or fall straight up or down. The slope is the ratio of changes in the y-coordinate to changes in the x-coordinate, which is undefined for a vertical line.