To find the remaining loan amount after 9 years, we can substitute \( x = 9 \) into the equation \( y = 15,413 - 1,635x \).
Calculating this:
\[ y = 15,413 - 1,635(9) \]
First, multiply \( 1,635 \) by \( 9 \):
\[ 1,635 \times 9 = 14,715 \]
Now substitute this back into the equation:
\[ y = 15,413 - 14,715 \]
Now, perform the subtraction:
\[ y = 698 \]
Thus, the remaining loan amount after 9 years is $698.