How do i show that the equation y-2=4(3x+5)is linear and then tell if it represents a proportional or nonproportional between x and y

If it can be represented in y=mx+b form, then it is definitley linear

the above equation is y=12x+22 so yes, it linear Its a freaking equation. If x is something and something, then it is y(As equations are). So if something is in an equation like above is definitley a proportional relationship.

examples of proportional relationships

y=(1)x(+0)
y=3x(+0)
Equations are always proportional. If you solve one and there is no solution(no logical relationship between x and y), then its not an equation