Y=-3+6and y=1/3x-8 determine if the equation are parallel, perpendicular or neither

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.