Respuesta :
For Parallelism condition; the slope are equal, i.e;
[tex]M_1=M_2[/tex]From the given straight line equation:
[tex]\begin{gathered} y=-\frac{2}{3}x+12 \\ M_1=-\frac{2}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{For Parallel lines:} \\ M_1=M_2 \\ \text{Thus, M}_2=-\frac{2}{3} \end{gathered}[/tex]From the given point (6, - 11);
[tex]x_1=6;y_1=-11[/tex]Since we have the given points and know the value of the slope, thus we have:
[tex]\begin{gathered} M_2=\frac{y-y_1}{x-x_1} \\ -\frac{2}{3}=\frac{y-(-11)}{x-6} \\ -\frac{2}{3}=\frac{y+11}{x-6} \\ \text{cross}-\text{multiply} \\ 3(y+11)=-2(x-6) \\ 3y+33=-2x+12 \\ 3y=-2x+12-33 \\ 3y=-2x-21 \\ \frac{3y}{3}=-\frac{2x}{3}-\frac{21}{3} \\ y=-\frac{2}{3}x-7 \end{gathered}[/tex]Hence, the correct option is A
