Final answer:
The correct equation of a line that is perpendicular to y = -3x + 2 and passes through the point (3, -1) is y = ⅓x - 2.
Step-by-step explanation:
The question involves finding the equation of a line that is perpendicular to a given line and passes through a specific point. The given equation of the line is y = -3x + 2. To be perpendicular, the new line must have a slope that is the negative reciprocal of the original slope of -3, which is ⅓. Hence, the slope of the line we are looking for is ⅓. Now, using the point (3, -1) that the new line passes through, we can use the point-slope form to find the equation:
y - y1 = m(x - x1) where (x1, y1) is the point (3, -1) and m is the slope ⅓.
Substituting these values, we get:
y + 1 = ⅓(x - 3)
Now, we distribute the slope on the right side:
y + 1 = ⅓x - 1
Subtracting 1 from both sides to solve for y:
y = ⅓x - 2
So, the correct equation of the line is y = ⅓x - 2, which corresponds to option D.