Subjects algebra

Gas Tank Rate C4Df95

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1. **State the problem:** We are given two points representing the gallons of gas in Aaron's car tank after driving a certain number of miles: (0, 17) and (144, 11). 2. **Find the rate of change (slope):** The rate of change tells us how many gallons of gas change per mile driven. The formula for slope $m$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (0, 17)$ and $(x_2, y_2) = (144, 11)$. 3. **Calculate the slope:** $$m = \frac{11 - 17}{144 - 0} = \frac{-6}{144}$$ 4. **Simplify the fraction:** $$m = \frac{\cancel{\text-6}}{\cancel{144}} = -\frac{1}{24}$$ 5. **Interpret the slope:** The slope $-\frac{1}{24}$ means that for every 24 miles driven, the gas decreases by 1 gallon. 6. **Complete the statement:** - $a = 24$ miles - $b = \text{decreases}$ - $c = 1$ gallon - $d = \text{less}$ **Final answer:** The rate of change means that for every 24 miles driven, the gas decreases by 1 gallon less.