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Create the equation of a line that is perpendicular to y+2=-3(x+2) and passes through the point (3,-6).

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Final answer:

To find the equation of a line that is perpendicular to a given line, we need to determine the negative reciprocal of the slope of the given line. The equation of the line that is perpendicular to y+2=-3(x+2) and passes through the point (3,-6) is y = 1/3x - 7.

Step-by-step explanation:

To find the equation of a line that is perpendicular to a given line, we need to determine the negative reciprocal of the slope of the given line.

The given line is y + 2 = -3(x + 2). Let's rewrite it in slope-intercept form: y = -3x - 8.

The slope of this line is -3, so the slope of the perpendicular line is 1/3.

Using the point-slope form of a line, we can write the equation of the perpendicular line passing through the point (3, -6) as:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

Substituting the values, we get: y - (-6) = 1/3(x - 3).

Simplifying the equation, we get: y + 6 = 1/3x - 1.

Final equation: y = 1/3x - 7.

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