1. **Problem:** Given that $a$ varies directly with $b$, and $a=56$ when $b=8$, find: a) The constant of proportionality $k$. b) The value of $a$ when $b=12$. 2. **Formula:** For direct variation, $a = kb$ where $k$ is the constant of proportionality. 3. **Step a:** Find $k$ using the given values: $$56 = k \times 8$$ Divide both sides by 8: $$k = \frac{56}{8} = 7$$ 4. **Step b:** Find $a$ when $b=12$ using $k=7$: $$a = 7 \times 12 = 84$$ **Answer:** a) The constant of proportionality $k$ is 7. b) When $b=12$, $a=84$.