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Find the slope of a line perpendicular to the line whose equation is 3x - 6y = -72. Fully simplify your...

Find the slope of a line perpendicular to the line whose equation is 3x - 6y = -72. Fully simplify your answer.

Answer

First, find the slope of the given line by rewriting the equation in slope-intercept form (y = mx + b).

Start with the equation: 3x - 6y = -72.

Solve for y:

  1. Subtract 3x from both sides: -6y = -3x - 72.
  2. Divide every term by -6: y = (1/2)x + 12.

The slope (m) of the given line is 1/2.

The slope of a line perpendicular to this line is the negative reciprocal of 1/2, which is -2.

Answer: -2

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