Solution
To write in slope-intercept form,
we use the formula
[tex]\begin{gathered} \frac{y_-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \\ \end{gathered}[/tex][tex]\begin{gathered} (x_1,y_1)=(-12,22) \\ \\ (x_2,y_2)=(-3,7) \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow\frac{y-22}{x+12}=\frac{7-22}{-3+12} \\ \\ \Rightarrow\frac{y-22}{x+12}=-\frac{15}{9} \\ \\ \Rightarrow\frac{y-22}{x+12}=-\frac{5}{3} \\ \\ \Rightarrow y-22=-\frac{5}{3}(x+12) \\ \\ \Rightarrow y-22=-\frac{5}{3}x-20 \\ \\ \Rightarrow y=-\frac{5}{3}x-20+22 \\ \\ \Rightarrow y=-\frac{5}{3}x+2 \end{gathered}[/tex]Correct option C