why you think this is important to use parenthese and give an example of this and also an example of NOT following this rule.

Question

I need to understand why it necessary to use parentheses in a linear equation and I would like examples of what both cases would look like. 

Answer 1

Parenthesis are very important in mathematical expressions because the expression inside a pair of parentheses is evaluated before continuing to evaluate the rest of the outer expression.  That's why Parentheses are first in the "order of precedence" list (P-E-M-D-A-S).
 
For example, if we have a linear equation like
      y = 4 + 4 / 2
  is the value of y=4 or is y=6 ??    (depending on whether you add first or divide first
 
Adding first, we have    y = (4 +4) / 2     and dividing firs, we have   y = 4 + (4 / 2)
 
Be sure that you understand the order of operations  (algebra will use variables and operators)
 
An equation like y = 4 * 4 / 2  doesn't need parenthesis.  Why?  because (remember P-E-M-D-A-S) multiplication is done before division.   (Also, multiplication and division are commutative.  But some other operations are not.)
 
And, an equation like y = 4 / 4 / 4  is confusing unless you perform operations at the same precedence level in a left-to-right order.  It is confusing (ambiguous) and gives either y=1/4 or y=4 depending on the order in which the operations are performed.  Therefore, the best rule is:  when there is any doubt, use parentheses !
 
Another interesting point:  various calculators require you to enter numbers and operators in unusual ways.  This is because calculators and computers make expressions precise by arranging terms and operators in an unambiguous way (this is called 'parsing' and Polish notation;  computer compilers and spreadsheets like Excel use this).