Chapter 4

For the following exercises, find the slope of the line that passes through the two given points. (2,4) and (4,10)

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy. $$ \begin{array}{|l|l|l|l|l|l|} \hline x & 8 & 15 & 26 & 31 & 56 \\ \hline y & 23 & 41 & 53 & 72 & 103 \\ \hline \end{array} $$

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted. Find the linear function that models the number of people inflicted with the common cold \(C\) as a function of the year, \(t\).

For the following exercises, find the slope of the line that passes through the two given points. (1,5) and (4,11)

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy. $$ \begin{array}{|l|l|l|l|l|l|} \hline x & 5 & 7 & 10 & 12 & 15 \\ \hline y & 4 & 12 & 17 & 22 & 24 \\ \hline \end{array} $$

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted. Find a reasonable domain and range for the function \(C\).

For the following exercises, find the slope of the line that passes through the two given points. (-1,4) and (5,2)

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy. $$ \begin{array}{|c|c|c|c|} \hline x & y & x & y \\ \hline 3 & 21.9 & 10 & 18.54 \\ \hline 4 & 22.22 & 11 & 15.76 \\ \hline 5 & 22.74 & 12 & 13.68 \\ \hline 6 & 22.26 & 13 & 14.1 \\ \hline 7 & 20.78 & 14 & 14.02 \\ \hline 8 & 17.6 & 15 & 11.94 \\ \hline 9 & 16.52 & 16 & 12.76 \\ \hline \end{array} $$

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted. If the function \(C\) is graphed, find and interpret the \(x\) - and \(y\) -intercepts.

For the following exercises, find the slope of the line that passes through the two given points. (8,-2) and (4,6)

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy. $$ \begin{array}{|c|c|} \hline x & y \\ \hline 4 & 44.8 \\ \hline 5 & 43.1 \\ \hline 6 & 38.8 \\ \hline 7 & 39 \\ \hline 8 & 38 \\ \hline 9 & 32.7 \\ \hline 10 & 30.1 \\ \hline 11 & 29.3 \\ \hline 12 & 27 \\ \hline 13 & 25.8 \\ \hline \end{array} $$

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted. If the function \(C\) is graphed, find and interpret the slope of the function.

For the following exercises, find the slope of the line that passes through the two given points. (6,11) and (-4,3)

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy. $$ \begin{array}{|l|l|l|l|l|l|l|} \hline x & 21 & 25 & 30 & 31 & 40 & 50 \\ \hline y & 17 & 11 & 2 & -1 & -18 & -40 \\ \hline \end{array} $$

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted. When will the output reach \(0 ?\)

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. \(f(-5)=-4,\) and \(f(5)=2\)

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy. $$ \begin{array}{|c|c|} \hline x & y \\ \hline 100 & 2000 \\ \hline 80 & 1798 \\ \hline 60 & 1589 \\ \hline 55 & 1580 \\ \hline 40 & 1390 \\ \hline 20 & 1202 \\ \hline \end{array} $$

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted. In what year will the number of people be \(9,700 ?\)

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. \(f(-1)=4,\) and \(f(5)=1\)

For the following exercises, use each set of data to calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to 3 decimal places of accuracy. $$ \begin{array}{|c|c|c|c|c|c|c|} \hline x & 900 & 988 & 1000 & 1010 & 1200 & 1205 \\ \hline y & 70 & 80 & 82 & 84 & 105 & 108 \\ \hline \end{array} $$

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. Passes through (2,4) and (4,10)

Graph \(f(x)=0.5 x+10 .\) Pick a set of five ordered pairs using inputs \(x=-2,1,5,6,9\) and use linear regression to verify that the function is a good fit for the data.

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. Passes through (1,5) and (4,11)

Graph \(f(x)=-2 x-10 .\) Pick a set of five ordered pairs using inputs \(x=-2,1,5,6,9\) and use linear regression to verify the function.

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. Passes through (-1,4) and (5,2)

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. Passes through (-2,8) and (4,6)

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. \(x\) intercept at (-2,0) and \(y\) intercept at (0,-3)

For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible. \(x\) intercept at (-5,0) and \(y\) intercept at (0,4)

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither. $$ \begin{array}{l} 4 x-7 y=10 \\ 7 x+4 y=1 \end{array} $$

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither. $$ \begin{array}{l} 3 y+x=12 \\ -y=8 x+1 \end{array} $$

For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in \(\underline{\text { Table }}\). 2. Assume that the house values are changing linearly. $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Mississippi } & \text { Hawaii } \\ \hline 1950 & \$ 25,200 & \$ 74,400 \\ \hline \end{array}$$ $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Mississippi } & \text { Hawaii } \\ \hline 2000 & \$ 71,400 & \$ 272,700 \\ \hline \end{array}$$ In which state have home values increased at a higher rate?

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither. $$ \begin{array}{l} 3 y+4 x=12 \\ -6 y=8 x+1 \end{array} $$

For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in \(\underline{\text { Table }}\). 2. Assume that the house values are changing linearly. $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Mississippi } & \text { Hawaii } \\ \hline 1950 & \$ 25,200 & \$ 74,400 \\ \hline \end{array}$$ $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Mississippi } & \text { Hawaii } \\ \hline 2000 & \$ 71,400 & \$ 272,700 \\ \hline \end{array}$$ If these trends were to continue, what would be the median home value in Mississippi in \(2010 ?\)

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither. $$ \begin{array}{l} 6 x-9 y=10 \\ 3 x+2 y=1 \end{array} $$

For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in \(\underline{\text { Table }}\). 2. Assume that the house values are changing linearly. $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Mississippi } & \text { Hawaii } \\ \hline 1950 & \$ 25,200 & \$ 74,400 \\ \hline \end{array}$$ $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Mississippi } & \text { Hawaii } \\ \hline 2000 & \$ 71,400 & \$ 272,700 \\ \hline \end{array}$$ If we assume the linear trend existed before 1950 and continues after \(2000,\) the two states' median house values will be (or were) equal in what year? (The answer might be absurd.)

For the following exercises, find the \(x\) - and \(y\) -intercepts of each equation. $$ f(x)=-x+2 $$

For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in Iable 3. Assume that the house values are changing linearly. $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Indiana } & \text { Alabama } \\ \hline 1950 & \$ 37,700 & \$ 27,100 \\ \hline 2000 & \$ 94,300 & \$ 85,100 \\ \hline \end{array}$$ In which state have home values increased at a higher rate?

For the following exercises, find the \(x\) - and \(y\) -intercepts of each equation. $$ g(x)=2 x+4 $$

For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in Iable 3. Assume that the house values are changing linearly. $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Indiana } & \text { Alabama } \\ \hline 1950 & \$ 37,700 & \$ 27,100 \\ \hline 2000 & \$ 94,300 & \$ 85,100 \\ \hline \end{array}$$ If these trends were to continue, what would be the median home value in Indiana in \(2010 ?\)

For the following exercises, find the \(x\) - and \(y\) -intercepts of each equation. $$ h(x)=3 x-5 $$

For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in Iable 3. Assume that the house values are changing linearly. $$\begin{array}{|c|c|c|} \hline \text { Year } & \text { Indiana } & \text { Alabama } \\ \hline 1950 & \$ 37,700 & \$ 27,100 \\ \hline 2000 & \$ 94,300 & \$ 85,100 \\ \hline \end{array}$$ If we assume the linear trend existed before 1950 and continues after \(2000,\) the two states' median house values will be (or were) equal in what year? (The answer might be absurd.)

For the following exercises, find the \(x\) - and \(y\) -intercepts of each equation. $$ k(x)=-5 x+1 $$

In \(2004,\) a school population was 1001. By 2008 the population had grown to 1697 . Assume the population is changing linearly. (a) How much did the population grow between the year 2004 and \(2008 ?\) (b) How long did it take the population to grow from 1001 students to 1697 students? (c) What is the average population growth per year? (d) What was the population in the year \(2000 ?\) (e) Find an equation for the population, \(P\), of the school \(t\) year after 2000 . (f) Using your equation, predict the population of the school in \(2011 .\)

For the following exercises, find the \(x\) - and \(y\) -intercepts of each equation. $$ -2 x+5 y=20 $$

In \(2003,\) a town's population was 1431. By 2007 the population had grown to 2134 . Assume the population is changing linearly. (a) How much did the population grow between the year 2003 and \(2007 ?\) (b) How long did it take the population to grow from 1431 people to 2134 people? c) What is the average population growth per year? (d) What was the population in the year \(2000 ?\) (e) Find an equation for the population, \(P\), of the town \(t\) years after 2000 . (f) Using your equation, predict the population of the town in 2014 .

For the following exercises, find the \(x\) - and \(y\) -intercepts of each equation. $$ 7 x+2 y=56 $$

A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $$\$ 71.50$$. If the customer uses 720 minutes, the monthly cost will be $$\$ 118 .$$ a) Find a linear equation for the monthly cost of the cell plan as a function of \(x,\) the number of monthly minutes used. b) Interpret the slope and \(y\) -intercept of the equation. c) Use your equation to find the total monthly cost if 687 minutes are used.

For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2 . Is each pair of lines parallel, perpendicular, or neither? Line 1: Passes through (0,6) and (3,-24) Line 2: Passes through (-1,19) and (8,-71)

A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $$\$ 10$$ and then a certain amount of money pei megabyte (MB) of data used on the phone. If a customer uses \(20 \mathrm{MB}\), the monthly cost will be $$\$ 11.20 .$$ If the customer uses \(130 \mathrm{MB}\), the monthly cost will be $$\$ 17.80$$. (a) Find a linear equation for the monthly cost of the data plan as a function of \(x,\) the number of \(\mathrm{MB}\) used. (b) Interpret the slope and \(y\) -intercept of the equation. c) Use your equation to find the total monthly cost if \(250 \mathrm{MB}\) are used.

For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2 . Is each pair of lines parallel, perpendicular, or neither? Line 1: Passes through (-8,-55) and (10,89) Line 2: Passes through (9,-44) and (4,-14)