Question

A line that is perpendicular to 3y = 11 - 8x has slope m=___

Answer 1

For a line that is parallel it is the same.
3y=11-8x
/3     /3
y=-8/3x+11/3
m=-8/3

For a line that is perpendicular, you flip the fraction and change the sign (if it is - make it +, if it is + make it -)
m=-8/3 for parallel, then:
m=3/8 for perpendicular