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In order to find the equation of the perpendicular line. Take into account that the realtion between the slopes of two perpendicular lines is given by:
[tex]m_1=-\frac{1}{m_2}[/tex]where m1 and m2 are the slopes of the lines.
The general form of the equation of a line is:
y = mx + b
where m is the slope and b the y-intercept. By comparing the previous equation with the given equation y = 1/3x + 12, you can notice that m=1/3.
If you take this slope as m2, then the slope of the perpendicular line is:
[tex]m_1=-\frac{1}{\frac{1}{3}}=-3[/tex]Next, consider that the equation of a line can be also written as follow:
y - yo = m(x - xo)
where (xo,yo) is a point of the line. In this case the point is (-6,-1).
Replace the values of xo, yo and m=m2, into the previous equation and solve for y:
y - (-1) = (-3)(x - (-6))
y + 1 = -3x - 18
y = -3x -19
Hence, the equation of the perpendicular line is y = -3x - 19