Final answer:
Option B) -6y = -2x + 12 is the line that is not perpendicular to the line y = 1/3x - 2 because, after rearranging it into slope-intercept form, it has a slope of 1/3, which is not the negative reciprocal of the original line's slope.
Step-by-step explanation:
The question asks which line is not perpendicular to the line y = 1/3x - 2. To be perpendicular, a line must have a slope that is the negative reciprocal of the original line's slope. The given line has a slope of 1/3, so the slope of a line perpendicular to it should be -3. Let's analyze the options provided.
- A) y = -3x is perpendicular to the given line because it has a slope of -3, which is the negative reciprocal of 1/3.
- B) -6y = -2x + 12. By rearranging this into slope-intercept form y = mx + b, we get y = (1/3)x - 2, which has a slope of 1/3, the same as the original line, so it is not perpendicular.
- C) 4y = -12x + 8. Converting this to slope-intercept form gives us y = -3x + 2, with a slope of -3, which is the negative reciprocal of 1/3, indicating it is perpendicular.
- D) y - 1 = -3(x + 2). In slope-intercept form, this is y = -3x - 5, which has a slope of -3 and thus is perpendicular to the given line.
Therefore, the line that is not perpendicular to the line y = 1/3x - 2 is option B) -6y = -2x + 12, because it has the same slope as the original line.