One cell phone plan costs $39.95 per month. the first 500 minutes of usage are free. each minute thereafter cost $.35. write a rule that describe the total monthly cost a function of the number of minutes of usage (over 500 minutes). then find the number of minutes of usage over 500 minutes for a bill of $69.70

Equation of cost per month: 39.95+0.35((x-500)=>0)=cost. (x=minutes of usage)

Explanation: The cell phone plan, at the start of a month costs $39.95, which is graph terms is the Y intercept. Thus the "39.95+" at the start of the equation. Since the first 500 minutes is free, then the cost of the plan must start after these 500 minutes, which is why there is a -500 for the amount of minutes used, but because the amount of minutes can be less than 500, which will result to a negative number (which can not happen, because these minutes are free), we must add a "greater than or equal to 0" sign at the end of t-500, so that the result must be 0 minutes or more. Since the cost of every minute after the first 500 minute costs $0.35, we must add that to the amount of minutes of usage that have passed, thus the 0.35x. All the results to 39.95+0.35((x-500)=>0)=cost in dollars

as for the bill of $67.70 questions, we simply have to plug this into the equation, making:
39.95+0.35((x-500)=>0)=$69.70
-39.95                           -39.95
0.35((x-500)=>)=$29.75
/0.35                    /0.35
x-500=85
+500    +500
x=585

So the answer is that it takes 585 minutes of usage to receive a bill of $69.70.