Any line with no slope is parallel to the
x-axis
y axis
line y=x

A line with no slope will be parallel to the y-axis, because a line with a slope of undefined means that the x-ordinates do not change in relation to the y-ordinates.
By using the gradient formula, , your x₁ and x₂ will yield the same value, thus forming a zero denominator.

As such, a vertical line will always have an undefined gradient, meaning that it has no slope at all.