91Ó°ÊÓ

The table shows the numbers \(y\) (in millions) of adults (over 18 years of age) never married in the United States for the years 2006 through \(2011 .\) $$ \begin{array}{|c|c|} \hline \text { Year } & \boldsymbol{y} \\ \hline 2006 & 55.3 \\ \hline 2007 & 56.1 \\ \hline 2008 & 58.3 \\ \hline 2009 & 59.1 \\ \hline 2010 & 61.5 \\ \hline 2011 & 63.3 \\ \hline \end{array} $$ A model for this data is \(y=1.63 t+45.1\), where \(t\) is the year, with \(t=6\) corresponding to 2006 . (Source: U.S. Census Bureau) (a) Plot the data and graph the model on the same set of coordinate axes. (b) Use the model to predict the number of adults over the age of 18 in 2020 who will never have married.

You purchase a boat for $$\$ 25,000$$. After 1 year, its depreciated value is $$\$ 22,700$$. The depreciation is linear. (a) Write a linear model that relates the value \(V\) of the boat to the time \(t\) in years. (b) Use the model to estimate the value of the boat after 3 years.

A sub shop purchases a used pizza oven for $$\$ 875$$. After 1 year, its depreciated value is $$\$ 790$$. The depreciation is linear. (a) Write a linear model that relates the value \(V\) of the oven to the time \(t\) in years. (b) Use the model to estimate the value of the oven after 5 years.

A city is paving a bike path. The same length of path is paved each day. After 4 days, 14 miles of the path remain to be paved. After 6 more days, 11 miles of the path remain to be paved. Find the average rate of change and use it to write a linear model that relates the distance remaining to be paved to the number of days.

A swimming pool already contains a small amount of water when you start filling it at a constant rate. The pool contains 45 gallons of water after 5 minutes and 120 gallons after 30 minutes. Find the average rate of change and use it to write a linear model that relates the amount of water in the pool to the time.

In Exercises \(39-44\), use the equations of the lines to determine whether the lines are parallel, perpendicular, or neither. Explain your reasoning. $$ \begin{aligned} &y_{1}=2 x-3 \\ &y_{2}=-\frac{1}{2} x+1 \end{aligned} $$

Let \(y\) represent the distance traveled by a car that is moving at a constant speed of 35 miles per hour. Let \(t\) represent the number of hours the car has traveled. Write an equation that relates \(y\) and \(t\), and sketch its graph.

A sales representative receives a monthly salary of $$\$ 2000$$ plus a commission of \(2 \%\) of the total monthly sales. Write a linear model that relates total monthly wages \(W\) to sales \(S\).

Explain how to find algebraically the \(x\)-intercept of the line given by \(y=m x+b\).

In Exercises \(61-64\), solve for \(y\) in terms of \(x\). $$ 4 x-5 y=-2 $$