Subjects algebra

Proportionality Check 8560B7

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1. **State the problem:** Determine if $y$ is proportional to $x$ based on the given table values: $$\begin{array}{c|cccc} x & 3 & 5 & 7 & 9 \\ y & 24 & 45 & 70 & 99 \end{array}$$ 2. **Recall the rule for proportionality:** Two variables $x$ and $y$ are proportional if there exists a constant $k$ such that $y = kx$ for all pairs $(x,y)$. 3. **Calculate the ratio $\frac{y}{x}$ for each pair:** $$\frac{24}{3} = 8$$ $$\frac{45}{5} = 9$$ $$\frac{70}{7} = 10$$ $$\frac{99}{9} = 11$$ 4. **Analyze the ratios:** Since the ratios are $8, 9, 10, 11$ and not equal, there is no single constant $k$ such that $y = kx$ for all values. 5. **Conclusion:** $y$ is **not proportional** to $x$ because the multiplier is not constant. **Final answer:** $y$ is not proportional to $x$.