Slope intercept form: y = mx + b
m = slope and b = y-intercept
The equation is: y = -3x + 6
The m value for this is -3, so the line has a slope of -3. If y = 1/3x - 8 was parallel to y = -3x + 6 then they would have the same slope, which they do not. So they aren't parallel.
The find the slope of a perpendicular line, take the negative reciprocal of the slope of y = -3x + 6. The negative reciprocal of -3 is 1/3. y = 1/3x - 8 has a slope of 1/3, so they are perpendicular to each other.
