The following table gives the projected state subsidies (in millions of dollars) to the Massachusetts Bay Transit Authority (MBTA) over a 5-yr period. $$ \begin{array}{lccccc} \hline \text { Year, } \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 \\ \hline \text { Subsidy, } \boldsymbol{y} & 20 & 24 & 26 & 28 & 32 \\ \hline \end{array} $$ a. Find an equation of the least-squares line for these data. b. Use the result of part (a) to estimate the state subsidy to the MBTA for the eighth year \((x=8)\).

The equation \(W=3.51 L-192\), expressing the relationship between the length \(L\) (in feet) and the expected weight \(W\) (in British tons) of adult blue whales, was adopted in the late \(1960 \mathrm{~s}\) by the International Whaling Commission. a. What is the expected weight of an 80 -ft blue whale? b. Sketch the straight line that represents the equation.

Moody's Corporation is the holding company for Moody's Investors Service, which has a \(40 \%\) share in the world credit-rating market. According to Company Reports, the total revenue (in billions of dollars) of the company is projected to be as follows \((x=0\) correspond to 2004\()\) : $$ \begin{array}{lccccc} \hline \text { Year } & 2004 & 2005 & 2006 & 2007 & 2008 \\ \hline \text { Revenue, } \boldsymbol{y} & 1.42 & 1.73 & 1.98 & 2.32 & 2.65 \\\ \hline \end{array} $$ a. Find an equation of the least-squares line for these data. b. Use the results of part (a) to estimate the rate of change of the revenue of the company for the period in question. c. Use the result of part (a) to estimate the total revenue of the company in 2010 , assuming that the trend continues.

At a unit price of \(\$ 55\), the quantity demanded of a certain commodity is 1000 units. At a unit price of \(\$ 85\), the demand drops to 600 units. Given that it is linear, find the demand equation. Above what price will there be no demand? What quantity would be demanded if the commodity were free?

Is there a difference between the statements "The slope of a straight line is zero" and "The slope of a straight line does not exist (is not defined)"? Explain your answer.

For each demand equation, where \(x\) represents the quantity demanded in units of 1000 and \(p\) is the unit price in dollars, (a) sketch the demand curve and (b) determine the quantity demanded corresponding to the given unit price \(p\). $$ p=-0.4 x+120 ; p=80 $$