Geometry Fundamentals: Slope 3

• Slope of Line A represents: $\dfrac{\Delta y}{\Delta x} = \dfrac{\Delta y}{0} \implies \text{Not defined}$

• Slope of Line B represents: $\dfrac{\Delta y}{\Delta x} = \dfrac{0}{\Delta x} \implies \boxed{0}$

In order to have a slope of 0, a line needs to have a change in $y,$ or a rise, of 0 because 0 divided by any number equals 0. Therefore, line B has a slope of 0 because it has a rise of 0.

Line A has an undefined slope. For any given change in $y,$ the change in $x$ is 0. Therefore, the slope would always be some number divided by 0. Because we can't divide by 0, the slope is undefined. Intuitively, this might make sense given that no line can be steeper than a vertical line. Therefore, its steepness is infinitely large.