Subjects algebra

Michaels Slope 4E7Ac6

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1. **State the problem:** We need to find the slope (rate of change) of Michael's graph using the given table of dollars and euros. 2. **Recall the formula for slope:** The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Choose two points from the table:** For example, use the first two points: $(40, 39)$ and $(80, 73)$. 4. **Calculate the slope:** $$m = \frac{73 - 39}{80 - 40} = \frac{34}{40}$$ 5. **Simplify the fraction:** $$m = \frac{\cancel{34}}{\cancel{40}} = \frac{17}{20}$$ 6. **Interpretation:** The slope $\frac{17}{20}$ means that for every 1 dollar increase, the cost in euros increases by $\frac{17}{20}$ euros. 7. **Verify with other points:** Using $(80, 73)$ and $(120, 107)$: $$m = \frac{107 - 73}{120 - 80} = \frac{34}{40} = \frac{17}{20}$$ This confirms the slope is consistent. **Final answer:** The slope (rate of change) of Michael's graph is $\frac{17}{20}$ euros per dollar.