Question

How do you identify equations as exponential growth, exponential decay, linear growth or linear decay `6x+5y=30`?

Answer 1

Your equation is a linear equation. The variable `x` is multiplied by a number only...no other operation is done on it.
You can check the "position" of `x` to decide if is:
1] a linear `(`number`)` `xx` `x`;
2] e exponential `(`number`)^(x)`;
Notice the difference in the "position" of `x`!!!
Have a look at this diagram:

In your case you have a linear [`(`number`)` `xx` `x` = `6x`] that can be written in `y=ax+b` form as:
`y=-6/5x+6`
So `a=-6/5<0` is a linear decay!

Hope it helps!