Chapter 5

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(0,-2), m=4$$

Write the equation in standard form with integer coefficients. $$x-5=0$$

Use the table which shows the number of movie theater screens (in thousands) from 1975 to 1995. $$ \begin{array}{|l|c|c|c|c|c|}\hline \text { Year } & 1975 & 1980 & 1985 & 1990 & 1995 \\\\\hline \text { Indoor screens (in thousands) } & 11 & 14 & 18 & 23 & 27 \\\\\hline \text { Drive-in screens (in thousands) } & 4 & 4 & 3 & 1 & 1 \\\\\hline\end{array} $$ Use the linear model to estimate the number of indoor movie screens in \(1989 .\) Did you use linear interpolation or linear extrapolation?

Write an equation in point-slope form of the line that passes through the given points. $$ (-2,-5),(7,-6) $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (1,4),(5,-1) $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(3,4), m=0$$

Write the equation in standard form with integer coefficients. $$y+3=0$$

Use the table which shows the number of dollars (in billions) spent on books and maps in the United States from 1990 through 1995. $$ \begin{array}{|l|c|c|c|c|c|c|}\hline \text { Years since 1990 } & 0 & 1 & 2 & 3 & 4 & 5 \\\\\hline \text { Billions of dollars } & 16.5 & 16.9 & 17.7 & 19.0 & 20.1 & 20.9 \\\\\hline\end{array} $$ Write a linear model for the amount spent on books and maps.

Write an equation in point-slope form of the line that passes through the given points. $$ (-9,10),(-4,-3) $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (-1,-2),(3,-2) $$

Write an equation of the line that passes through the point and has the given slope. Write the equation in slope-intercept form. $$(-2,4), m=0$$

Write the equation in standard form with integer coefficients. $$x-5=0$$

Write an equation in point-slope form of the line that passes through the given points. $$ (4,-5),(-2,-7) $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (2,0),(-2,6) $$

Write the equation in standard form with integer coefficients. $$y=3 x-8$$

Use the table which shows the number of dollars (in billions) spent on toys and sport supplies in the United States from 1990 through 1995. $$ \begin{array}{|c|c|}\hline \text { Years since 1990 } & \text { Billions of dollars } \\\\\hline 0 & 31.6 \\\\\hline 1 & 32.8 \\\\\hline 2 & ? \\\\\hline 3 & 36.5 \\\\\hline 4 & 40.1 \\\\\hline 5 & 42.7 \\\\\hline\end{array} $$ Write a linear model for the amount spent on toys and sport supplies.

Write an equation in point-slope form of the line that passes through the given points. $$ (-5,10),(-4,-2) $$

As people grow older, the size of their pupils tends to get smaller. The average diameter (in millimeters) of one person's pupils is given in the table. $$ \begin{array}{|c|c|c|} \hline {\text { Sample Pupil Diameters }} \\ \text { Age (years) } & \text { Day } & \text { Night } \\ \hline 20 & 4.7 & 8.0 \\ \hline 30 & 4.3 & 7.0 \\ \hline 40 & 3.9 & 6.0 \\ \hline 50 & 3.5 & 5.0 \\ \hline 60 & 3.1 & 4.1 \\ \hline 70 & 2.7 & 3.2 \\ \hline 80 & 2.3 & 2.5 \\ \hline \end{array} $$ Draw a scatter plot of the day diameters and another of the night diameters. Let \(x\) represent the person's age and let \(y\) represent pupil diameters.

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (2,-3),(-3,7) $$

Use the table which shows the number of dollars (in billions) spent on toys and sport supplies in the United States from 1990 through 1995. $$ \begin{array}{|c|c|}\hline \text { Years since 1990 } & \text { Billions of dollars } \\\\\hline 0 & 31.6 \\\\\hline 1 & 32.8 \\\\\hline 2 & ? \\\\\hline 3 & 36.5 \\\\\hline 4 & 40.1 \\\\\hline 5 & 42.7 \\\\\hline\end{array} $$ Use the linear model to estimate the amount spent in \(1992 .\) Did you use linear interpolation or linear extrapolation?

Write the equation in standard form with integer coefficients. $$y=-0.4 x+1.2$$

Write an equation in point-slope form of the line that passes through the given points. $$ (-3,-2),(-3,-8) $$

As people grow older, the size of their pupils tends to get smaller. The average diameter (in millimeters) of one person's pupils is given in the table. $$ \begin{array}{|c|c|c|} \hline {\text { Sample Pupil Diameters }} \\ \text { Age (years) } & \text { Day } & \text { Night } \\ \hline 20 & 4.7 & 8.0 \\ \hline 30 & 4.3 & 7.0 \\ \hline 40 & 3.9 & 6.0 \\ \hline 50 & 3.5 & 5.0 \\ \hline 60 & 3.1 & 4.1 \\ \hline 70 & 2.7 & 3.2 \\ \hline 80 & 2.3 & 2.5 \\ \hline \end{array} $$ Find an equation of the line that closely fits the day and the night sets of data for pupil diameters.

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (0,-5),(3,4) $$

In Exercises 26 and 27 , use the following information. In 1990 the population of South Carolina was approximately \(3,486,000 .\) During the next five years, the population increased by approximately \(37,400\) people per year. Write an equation to model the population \(P\) of South Carolina in terms of \(t\) the number of years since 1990 .

Write the equation in standard form with integer coefficients. $$3 x+9=\frac{7}{2} y$$

Write an equation in point-slope form of the line that passes through the given points. $$ (-3,-9),(-6,-8) $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (6,-4),(-1,2) $$

Use the table which shows the average tuition for attending a private and a public four-year college. $$ \begin{array}{|c|c|c|}\hline \text { Year } & \text { Public college } & \text { Private college } \\\\\hline 1990 & \$ 2,035 & \$ 10,348 \\\\\hline 1991 & \$ 2,159 & \$ 11,379 \\\\\hline 1992 & \$ 2,410 & \$ 12,192 \\\\\hline 1993 & \$ 2,604 & \$ 13,055 \\\\\hline 1994 & \$ 2,820 & \$ 13,874 \\\\\hline 1995 & \$ 2,977 & \$ 14,537 \\ \hline 1996 & \$ 3,151 & \$ 15,581 \\\\\hline\end{array} $$ Write a linear model of the tuition for attending a public and of the tuition for attending a private college.

Write the equation in standard form with integer coefficients. $$y=9 x+\frac{1}{2}$$

Write an equation in point-slope form of the line that passes through the given points. $$ (-3,-7),(-4,-8) $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (-2,-1),(8,8) $$

A rental company charges a flat fee of \(\$ 30\) and an additional \(\$ .25\) per mile to rent a moving van. Write an equation to model the total charge \(y\) (in dollars) in terms of \(x,\) the number of miles driven.

Write the equation in standard form with integer coefficients. $$y=\frac{5}{2} x+9$$

Write an equation in point-slope form of the line that passes through the given points. $$ (1,-7),(-1,-5) $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (1,1),(7,4) $$

Write the equation in standard form with integer coefficients. $$y=-\frac{3}{4} x+\frac{5}{4}$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (-1,-3), m=4 $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (2,4),(1,-2) $$

Write a linear equation to model the situation. Use unit analysis to check your model. You borrow \(\$ 40\) from your sister. To repay the loan, you pay her \(\$ 5\) a week.

Write an equation of the line that has the given \(x\) -intercept and slope. $$x \text { -intercept }=2, m=-\frac{2}{3}$$

Use the following information. You are the produce manager at a new grocery store. It is your job to decide how much fruit to order for the week of the grand opening. You find a table that shows yearly per person consumption of pounds of bananas. $$ \begin{array}{|c|c|}\hline \text { Year } & \text { Pounds of bananas } \\\\\hline 1990 & 24.4 \\\\\hline 1991 & 25.1 \\\\\hline 1992 & 27.3 \\\\\hline 1993 & 26.8 \\\\\hline 1994 & 28.1 \\\\\hline 1995 & 27.4 \\\\\hline \end{array} $$ What was the average weekly consumption per person of bananas in \(1995 ?\) What was the average monthly consumption?

Write the equation in standard form with integer coefficients. $$y=-\frac{1}{7} x+\frac{6}{7}$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (-6,2), m=-5 $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (5,-6),(5,-3) $$

Write a linear equation to model the situation. Use unit analysis to check your model. Your uncle weighed 180 pounds. He has lost 2 pounds a month for 8 months.

Write an equation of the line that has the given \(x\) -intercept and slope. $$x \text{-intercept} =4, m=3$$

Write the equation in standard form with integer coefficients. $$y=-\frac{1}{3} x-4$$

Write an equation in point-slope form of the line that passes through the given point and has the given slope. $$ (-10,0), m=2 $$

Graph the points and draw a line through them. Write an equation in slope- intercept form of the line that passes through the points. $$ (-3,-5),(1,9) $$