first, we know it will be perpendicular to a line with a slope -3/4
and a line to be perpendicular must be inverse and with an inverted sign, so the slope of our line is: 4/3
so the slope form is:
[tex]y=\frac{4}{3}x+b[/tex]
and we can find b replacing x and y for the point (12,9)
[tex]\begin{gathered} 9=\frac{4}{3}\cdot12+b \\ 9=16+b \\ b=9-16=7 \end{gathered}[/tex]
so the answer is: Option A
[tex]y=\frac{4}{3}x-7[/tex]
