If the equation of a line is given by y = 3x - 6, what is a possible slope of a line perpendicular to it?

To understand why -1/3 is the correct choice for the slope of a line perpendicular to the line given by the equation y = 3x - 6, we first need to identify the slope of the original line. In the equation y = 3x - 6, the slope is 3.

Law of perpendicularity states that the slopes of two perpendicular lines are negative reciprocals of each other. This means that if one line has a slope of m, then a line perpendicular to it will have a slope of -1/m.

In this case, taking the negative reciprocal of the slope 3:

1. The reciprocal of 3 is 1/3.

2. Changing the sign gives us -1/3.

Therefore, the slope of a line that is perpendicular to the original line must be -1/3.

This makes -1/3 the correct answer since it meets the condition of being the negative reciprocal of 3. The other options either do not provide the correct sign or do not represent the negative reciprocal of 3.