Chapter 2

Compare the slope-intercept form with the point-slope form. Give examples of each.

Business \(A\) company manufactures compact discs with recorded music. The master disc costs \(\$ 2000\) to produce and copies cost \(\$ 0.45\) each. If a company spent \(\$ 2990\) producing compact discs, how many copies did the company manufacture?

Give an example of two quantities in real life that vary directly. Explain your answer. Use an equation to describe the relationship between the two quantities.

Explain how you would find the equation of a line passing through two points. Give an example.

Exercises 121 and 122: The following data can be modeled by a linear function. Estimate the value of \(x\) when \(y=2.99\) $$ \begin{array}{ccccc} x & 2 & 4 & 6 & 8 \\ \hline y & 0.51 & 1.23 & 1.95 & 2.67 \end{array} $$

Exercises 121 and 122: The following data can be modeled by a linear function. Estimate the value of \(x\) when \(y=2.99\) $$ \begin{array}{ccccc} x & 1 & 2 & 3 & 4 \\ \hline y & -1.66 & 2.06 & 5.78 & 9.50 \end{array} $$

Ring Size \(\quad\) The table lists ring size \(S\) for a finger with circumference \(x\) in centimeters. $$ \begin{array}{ccccc} x(\mathrm{cm}) & 4.65 & 5.40 & 5.66 & 6.41 \\ S(\text { size }) & 4 & 7 & 8 & 11 \end{array} $$ Source: Overstock (a) Find a linear function \(S\) that models the data. (b) Find the circumference of a finger with a ring size of 6

Hat Size The table lists hat size \(H\) for a head with circumference \(x\) in inches. $$ \begin{array}{ccccc} x \text { (in.) } & 21 \frac{1}{8} & 21 \frac{7}{8} & 22 \frac{5}{8} & 25 \\ \hline S \text { (size) } & 6_{4}^{3} & 7 & 7 \frac{1}{4} & 8 \end{array} $$ Source: Brentblack, (a) Find a linear function \(S\) that models the data. (b) Find the circumference of a head with a hat size of \(7 \frac{1}{2}\)

Super BowlAds The table lists the cost in millions of dollars for a 30 -second Super Bowl commercial for selected years. $$ \begin{array}{lccccc} \text { Year } & 1990 & 1994 & 1998 & 2004 & 2008 \\ \hline \text { Cost } & 0.8 & 1.2 & 1.6 & 2.3 & 2.7 \end{array} $$ Source: MSNBC. (a) Find a linear function \(f\) that models the data. (b) Estimate the cost in 1987 and compare the estimate to the actual value of \(\$ 0.6\) million. Did your estimate involve interpolation or extrapolation? (c) Use \(f\) to predict the year when the cost could reach \(\$ 3.2\) million.

Women in Politics The table lists the percentage \(P\) of women in state legislatures during year \(x .\) $$ \begin{array}{|c|ccccc} \hline x & 1993 & 1997 & 2001 & 2005 & 2007 \\ \hline P & 20.5 & 21.6 & 22.4 & 22.7 & 23.5 \\ \hline \end{array} $$ Source: National Women's Political Caucus. (a) Find a linear function \(P\) that models the data. (b) Estimate this percentage in 2003 and compare the estimate to the actual value of \(22.4 \% .\) Did your estimate involve interpolation or extrapolation? (c) Use \(P\) to predict the year when this percentage could reach \(25 \%\)

Describe a basic graphical method used to solve a linear equation. Give examples.

Describe verbally how to solve ax + b = 0. What assumptions have you made about the value of a?