You didn't make a mistaken. The linear regression line isn't going to fit your data points exactly. How can it? I mean if it did, then it would be a sure bet that you would be able to find an equation relating additive to miles (km) per gallon without even using a calculator.
Not sure how you calculated i t manually, however using the trusty TI, I got the same results that you did.
Do you know how to create a scatter plot on the TI? If you do a scatter plot, as well as the linear regression equation, you'll be able to see how things match up.