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.
Gas Tank Rate C4Df95
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.