Write an equation of the line that passes through $\left(7,10\right)$ and is perpendicular to the line $y=\frac{1}{2}x-9$ .

You just purchased two coins at a price of $670 each. because one of the coins is more collectible, you believe that its value will increase at a rate of 7.1 percent per year, while you believe the second coin will only increase at 6.5 percent per year. if you are correct, how much more will the first coin be worth in 15 years?