Final answer:
To find an equation parallel to the given line, use the same slope. To find an equation perpendicular to the given line, use the negative reciprocal of its slope.
Step-by-step explanation:
To find an equation parallel to the given line, we know that parallel lines have the same slope. The given line has a slope of 3, so the equation of the parallel line will also have a slope of 3.
Using the point-slope form of a linear equation, we can write the equation as y - (-2) = 3(x - 3). Simplifying this equation gives us y + 2 = 3x - 9.
To find an equation perpendicular to the given line, we need to use the negative reciprocal of its slope.
The negative reciprocal of 3 is -1/3. Using the point-slope form again, the equation of the perpendicular line becomes y - (-2) = -1/3(x - 3). Simplifying this equation gives us y + 2 = -1/3x + 1.