1. **State the problem:** We have two lines given by the equations $y = ax + b$ and $y = -bx$. They intersect at the point $(2,8)$. We need to find the value of $a$. 2. **Use the fact that the point $(2,8)$ lies on both lines:** For the first line: $$8 = a \cdot 2 + b \implies 8 = 2a + b$$ For the second line: $$8 = -b \cdot 2 \implies 8 = -2b$$ 3. **Solve for $b$ from the second equation:** $$8 = -2b \implies b = \frac{\cancel{8}}{\cancel{-2}} = -4$$ 4. **Substitute $b = -4$ into the first equation:** $$8 = 2a + (-4) \implies 8 = 2a - 4$$ 5. **Solve for $a$:** $$8 + 4 = 2a \implies 12 = 2a \implies a = \frac{\cancel{12}}{\cancel{2}} = 6$$ **Final answer:** $a = 6$ which corresponds to option C).