Why will the slope of any horizontal line be 0? Why will the slope of any vertical line be undefined? Complete the answers. the slope of a horizontal line will always be 0 because the y-coordinates of any two points be . therefore the in the slope formula will always be 0.the slope of a vertical line will always be undefined because the x-coordinates of anytwo points will be. therefore the the in the slope formula will always be 0 since you cannot divide by 0 the slope will always be undefined