STEP 1
Write out the formula needed
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Also, m=}\frac{y_{}-y_1}{x_{}-x_1} \end{gathered}[/tex]STEP 2
Equate both equations together then substitute the values of the points into the equation.
[tex]\begin{gathered} \frac{y_2-y_1}{x_2-x_1}=\frac{y_{}-y_1}{x_{}-x_1} \\ \frac{-14-(-2)}{3-(-5)}=\frac{y-(-2)}{x-(-5)} \\ \frac{-14+2}{3+5}=\frac{y+2}{x+5} \\ -\frac{12}{8}=\frac{y+2}{x+5} \\ -\frac{3}{2}=\frac{y+2}{x+5} \\ \text{Cross multiply} \\ -3(x+5)=2(y+2) \\ -3x-15=2y+4 \\ 2y=-3x-15-4 \\ 2y=-3x-19 \\ \text{Divide both sides by 2} \\ y=-\frac{3x}{2}-\frac{19}{2} \end{gathered}[/tex]