## Precalculus (6th Edition) Blitzer

The slope of a line can be defined as the ratio of the vertical change to the horizontal change when moving from one fixed point to another along a line. The general notation for the slope of a line is, $\left( m \right)$ is given by $\text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}}$ Let $\left( {{x}_{1}},{{y}_{1}} \right)$ represents point $\left( a,b \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ represents point $\left( a,b+c \right)$ Then, \begin{align} & \text{m= }\frac{\text{change in vertical}}{\text{change in horizontal}} \\ & =\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & =\frac{\left( \left( b+c \right)-b \right)}{a-a} \\ & =\frac{c}{0} \end{align} Hence, the slope of the line is undefined. As slope of the line passing through the provided pair of points is not defined, therefore the line is vertical.