1. **State the problem:** We have a function $f(x) = -ax + b$ where $a$ and $b$ are constants. The graph of $y = f(x) - 15$ has a y-intercept at $(0, 99)$. The product $ab = \frac{65}{7}$. We need to find the value of $a$. 2. **Use the y-intercept information:** At the y-intercept, $x=0$, so $$y = f(0) - 15 = b - 15 = 99$$ 3. **Solve for $b$:** $$b - 15 = 99$$ $$b = 99 + 15 = 114$$ 4. **Use the product $ab = \frac{65}{7}$:** $$a \times b = \frac{65}{7}$$ Substitute $b=114$: $$a \times 114 = \frac{65}{7}$$ 5. **Solve for $a$:** $$a = \frac{65}{7 \times 114} = \frac{65}{798}$$ 6. **Simplify the fraction:** Both numerator and denominator are divisible by 13: $$a = \frac{\cancel{13} \times 5}{\cancel{13} \times 61.3846}$$ Since 114 is not divisible by 13 exactly, let's check carefully: 114 divided by 13 is $8.769$, so no. Try dividing numerator and denominator by 13: 65 divided by 13 is 5. 798 divided by 13 is 61.3846 (not integer), so no. Try dividing numerator and denominator by 1 only. So fraction stays as $\frac{65}{798}$. 7. **Final answer:** $$\boxed{\frac{65}{798}}$$