1. The problem involves understanding the relationships between variables $b$ and $m$ given by three equations and their corresponding tables and graphs. 2. The first equation is $$b = m + 8$$ where $b$ is the dependent variable and $m$ is the independent variable. 3. According to the table, when $b=1$, $m=8$. Let's check this: $$1 = 8 + 8 = 16$$ which is false, so the table data does not match the equation. 4. The graph shows that when $b$ increases by 1, $m$ increases by 1. From the equation, increasing $m$ by 1 increases $b$ by 1, which matches the graph description. 5. The second equation is $$m = 8b$$ where $m$ is dependent and $b$ is independent. 6. The table shows when $b=1$, $m=8$, which fits the equation: $$m = 8 \times 1 = 8$$ 7. The graph shows that when $b$ increases by 1, $m$ increases by 8, consistent with the equation. 8. The third equation is $$b = 8m$$ where $b$ is dependent and $m$ is independent. 9. The table shows when $b=1$, $m=9$. Check if this fits: $$1 = 8 \times 9 = 72$$ which is false, so the table data does not match the equation. 10. The graph shows when $b$ increases by 1, $m$ increases by 8, which contradicts the equation since $b$ depends on $m$ multiplied by 8. Summary: - Equation 1: $b = m + 8$ does not match the table but matches the graph increment. - Equation 2: $m = 8b$ matches both table and graph. - Equation 3: $b = 8m$ does not match the table or graph increments. Final conclusion: Only the second equation $m = 8b$ correctly represents the relationship described by both the table and the graph.