i am to consider the line -x-3y=2 what is the parallel line slope and the perpendicular line slope

-x - 3y = 2

-3y = x + 2
y = (-1/3)x - 2/3

slope of the given line or any line parallel to it is -1/3
slope of a perpendicular is 3

To find the slope of a line, we need to rewrite the equation in slope-intercept form, which is y = mx + b, where m represents the slope.

Given the equation -x - 3y = 2, let's rearrange it in slope-intercept form:
-3y = x + 2 (add x to both sides)
y = -1/3x - 2/3 (divide by -3)

In this form, the slope (m) is the coefficient next to x, which is -1/3. So, the slope of the line -x - 3y = 2 is -1/3.

Now, for a line to be parallel to another line, it must have the same slope. Therefore, the equation of the parallel line would also have a slope of -1/3.

To find the slope of a line perpendicular to a given line, we need to take the negative reciprocal of the given slope. The negative reciprocal of -1/3 would be 3/1 or simply 3. So, the slope of the perpendicular line would be 3.