The given point is (6,-11) and the given line is,
[tex]y=-\frac{2}{3}x+12[/tex]
Comparing to point intercept form y=mx+c the slope of the given line is,
m=-2/3.
The required line is parallel to the given line hence the slope of the required line will be -2/3.
The equation of the line can be determined as,
[tex]\begin{gathered} \frac{y-(-11)}{x-6}=\frac{-2}{3} \\ 3(y+11)=-2(x-6) \\ y+11=\frac{-2}{3}(x-6) \\ y=\frac{-2}{3}x+4-11 \\ y=\frac{-2}{3}x-7 \end{gathered}[/tex]
Thus, option (A) is the correct solution.
