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.