Answer:
The equation of the perpendicular line is y=-3x-15.
Explanation:
Given the line y=1/3x+6
Comparing it with the slope-intercept form: y=mx+b
[tex]\text{Slope}=\frac{1}{3}[/tex]Let the slope of the perpendicular line = m
Two lines are perpendicular if the product of their slopes is -1.
Therefore:
[tex]\begin{gathered} \frac{1}{3}m=-1 \\ m=-3 \end{gathered}[/tex]To find the equation of the perpendicular line passing through (-9, 12), we use the point-slope form.
[tex]y-y_1=m(x-x_1)[/tex]Substituting the slope and point (-9,12), we have:
[tex]\begin{gathered} y-12=-3(x-(-9)) \\ y-12=-3(x+9) \\ y-12=-3x-27 \\ y=-3x-27+12 \\ y=-3x-15 \end{gathered}[/tex]The equation of the perpendicular line is y=-3x-15.
