Answer
The value of the expression $\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ is $3$.
Work Step by Step
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 $\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=3$
