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Find the slope of a line perpendicular to the line whose equation is 3x - 12y = -108. Fully simplify your...

Find the slope of a line perpendicular to the line whose equation is 3x - 12y = -108. Fully simplify your answer.

Answer

First, convert the equation 3x - 12y = -108 to slope-intercept form (y = mx + b) to find the slope of the given line.

Rearrange the equation: 3x - 12y = -108 becomes -12y = -3x - 108.
Divide every term by -12: y = (1/4)x + 9.
The slope (m) of the given line is 1/4.
The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore, the perpendicular slope is -4.

Answer: -4

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