2. the table shows the distance a car drove on one tank of gas.\nmiles driven gas used (gal)\n0 0\n60 2\n150…

Explanation:

Step1: Recall rate - of - change formula

The rate of change formula is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y$ is miles driven and $x$ is gas used.

Step2: Calculate rate of change for each interval

For the interval from $(0,0)$ to $(2,60)$: $\frac{60 - 0}{2 - 0}=\frac{60}{2}=30$ miles per gallon. For the interval from $(2,60)$ to $(5,150)$: $\frac{150 - 60}{5 - 2}=\frac{90}{3}=30$ miles per gallon. For the interval from $(5,150)$ to $(6,170)$: $\frac{170 - 150}{6 - 5}=\frac{20}{1}=20$ miles per gallon. For the interval from $(6,170)$ to $(9,230)$: $\frac{230 - 170}{9 - 6}=\frac{60}{3}=20$ miles per gallon. For the interval from $(9,230)$ to $(11,280)$: $\frac{280 - 230}{11 - 9}=\frac{50}{2}=25$ miles per gallon.

Step3: Identify the least rate

The least rate of change (gas - mileage) is 20 miles per gallon, which occurs in the intervals from $(5,150)$ to $(6,170)$ and from $(6,170)$ to $(9,230)$.

Answer:

The rate of change is least between $(5,150)$ and $(6,170)$ and between $(6,170)$ and $(9,230)$ with a rate of 20 miles per gallon.