Final answer:
The line that is perpendicular to y = -3x + 2 is the one with a slope of 1/3. After comparing the slopes of all options, D) x - 3y = 3 is the line with the required slope and the correct answer.
Step-by-step explanation:
To determine which line is perpendicular to the line y = -3x + 2, we need to look at the slopes of the potential lines. Two lines are perpendicular if the product of their slopes is -1. The slope of the given line is -3. Therefore, we are looking for a line with a slope of 1/3, since -3 times 1/3 equals -1.
Let's analyze each option:
A) 3x + y = 4 can be rewritten as y = -3x + 4, which has a slope of -3. This is not perpendicular as its slope is not 1/3.
B) x + 3y = 24 can be rewritten as y = -1/3x + 8, which has a slope of -1/3. This is not perpendicular as well because we need a positive 1/3 slope.
C) 3x - y = 5 can be rewritten as y = 3x - 5, which has a slope of 3. This is not perpendicular either.
D) x - 3y = 3 can be rewritten as y = 1/3x - 1, which has a slope of 1/3. This line is perpendicular to the given line y = -3x + 2.
Therefore, the correct answer is D) x - 3y = 3, as it has the required slope of 1/3 to be perpendicular to the line y = -3x + 2.