To find the equation perpendicular to y = -3x + 1 through the point (3, -2), the slope of the line is 1/3. Therefore, the equation would be y = 1/3x - 3. For an equation through the point (-2, 3) and parallel to y = -3x - 1, the equation would be y = -3x - 3.
To find an equation perpendicular to y = -3x + 1 through the point (3, -2), we first need to find the slope of the given equation.
The slope of the given equation is -3.
The slope of a perpendicular line is the negative reciprocal of the original slope.
Therefore, the slope of the perpendicular line is 1/3.
Using the point-slope form of an equation, we can plug in the values: y - y1 = m(x - x1).
Substituting (3, -2) and slope 1/3, we get y - (-2) = 1/3(x - 3). Simplifying further, we get y + 2 = 1/3x - 1.
Rearranging the equation, we get y = 1/3x - 3, which is the equation perpendicular to y = -3x + 1 through the point (3, -2).
For an equation through the point (-2, 3) and parallel to y = -3x - 1, the slope of the parallel line will be the same as the slope of y = -3x - 1, which is -3.
Using the point-slope form again, we substitute (-2, 3) and slope -3 into the equation.
This gives us y - 3 = -3(x - (-2)).
Simplifying further, we get y - 3 = -3(x + 2).
Rearranging the equation, we get y = -3x - 3, which is the equation through the point (-2, 3) and parallel to y = -3x - 1.