$($Preview Activity $1\mathrm{.}5\mathrm{.}1)$ A car leaves town $($at time $\backslash ($ t$=0\backslash ))$ and heads east on the highway. Its position in miles from town is given by the graph of the function $\backslash ($ y$=$s$($t$)\backslash )$ below. Three important points are labeled on the graph; where the graph looks linear, assume that it is indeed a straight line.

a$.$ In everyday language, describe the behavior of the car over the time intervals $[0,57],[57,68\backslash (]\backslash ),$ and $\backslash ([68,104]\backslash ).$

b$.$ Find the slope of the line between the points $\backslash ((57,63\mathrm{.}8)\backslash )$ and $\backslash ((104,106\mathrm{.}8)\backslash ).$ What are the units on this slope? What does the slope represent in the context of the car?

c$.$ Find the average rate of change of the car's position on the interval $[68,104].$ Include units on your answer.

d$.$ Estimate the instantaneous rate of change of the car's position when $\backslash ($ t$=80\backslash ).($In other words, estimate $\backslash ($ s$^\{\backslash$prime$\}(80)\backslash ).)$ Write a sentence to explain your reasoning and the meaning of this value.