Shirley has already jogged 5 miles. She continues to jog at an average rate of 3.5 miles per hour. This situation is modeled by the function y=3.5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary.

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.