1. The problem asks to find the equation that represents the hanger diagram described. 2. The diagram consists of a vertical yellow rectangular bar labeled 9 on the inside left. 3. To the right of the bar, there is a vertical stack of eight alternating red and orange diamonds. 4. The red diamonds contain the letter $z$ and the orange diamonds contain the number 2. 5. Since the diamonds alternate and there are eight diamonds total, there are 4 red diamonds with $z$ and 4 orange diamonds with 2. 6. The total value represented by the diamonds is the sum of the values of the red and orange diamonds. 7. The red diamonds contribute $4z$ and the orange diamonds contribute $4 \times 2 = 8$. 8. The hanger diagram balances the yellow bar labeled 9 with the sum of the diamonds. 9. Therefore, the equation representing the hanger diagram is: $$9 = 4z + 8$$ 10. This equation shows that the weight 9 on the left balances the combined weight of the diamonds on the right. Final answer: $$9 = 4z + 8$$