## Precalculus (6th Edition) Blitzer

The value of the expression $\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ is $3$.
Consider the coordinates: $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -3,1 \right)\text{ and }\left( {{x}_{2}},{{y}_{2}} \right)=\left( -2,4 \right)$ The objective is to calculate $\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ if $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -3,1 \right)\text{ and }\left( {{x}_{2}},{{y}_{2}} \right)=\left( -2,4 \right)$ Therefore, substitute the coordinates in the equations $\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ Therefore, \begin{align} & \frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\frac{4-1}{-2-\left( -3 \right)} \\ & =\frac{3}{-2+3} \\ & =3 \end{align} Therefore, the required solution is $\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=3$