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What is the equation of the lime that is perpendicular to y=1/3x+12 that contains the point (-6,-1)

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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:


m_1=-(1)/(m_2)

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:


m_1=-(1)/((1)/(3))=-3

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

User Kit Plummer
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