1) The line y=5 is an horizontal line, as it has the same value of y for any value of x.
Being an horizontal line, is parallel to the x-axis (which is also defined by the equation y=0).
2) With the slope defined as the rate of change of y with respect to x, a vertical line has an infinite rate of change, as even the smallest change in x, will trigger an infinite change in y.
Also, we can not define the sign of the slope, as we do not know if y increases or decreases with an increase in x.
That is why the slope of a vertical line is undefined.
3) With same definition of the slope (the rate of change of y with respect to x), an horizontal line does not show change in the value of y when we have changes in the x value.
Then, as we have no change, the value of the slope of an horizontal line is zero.
