Answer:
parallel: m = 1/3
perpendicular: m = -3
Explanation:
Parallel line:
Slopes of parallel lines are equal.
If the given line has slope 1/3, then the parallel line also has slope 1/3.
Perpendicular line:
The slopes of perpendicular lines are negative reciprocals. That means that the product of the slopes is -1. That also means that to find the slope of a perpendicular line to a given line, first find the reciprocal of the slope of the given line (flip the fraction), then change the sign.
The slope of the perpendicular line and the slope of the line must multiply to -1.
Start with the given slope, 1/3. Now flip it to get 3/1 which is simply 3. Now change the sign to -3. The slope of the perpendicular is -3.
Check: multiply the slopes. They must have a product of -1.
1/3 * (-3) = 1/3 * (-3/1) = -3/3 = -1
The product is -1, so the slope of the perpendicular, -3, is correct.