Section 1
Reading Graphs, Plotting Points, and Scaling Graphs
Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.$$(-9,3),(-2,-1),(1,5)$$CAN'T COPY THE GRAPH
Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.$$(-2,-1),(1,5),(7,3)$$CAN'T COPY THE GRAPH
Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.$$(-2,-9),(2,1),(4,-6)$$CAN'T COPY THE GRAPH
Reinforcement In each of Exercises $1-4$ match the set of coordinates with the graph from (a)-(d) below that would be the best for plotting the points.$$(-2,-1),(-9,3),(-4,-6)$$CAN'T COPY THE GRAPH
Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count asone drink.CAN'T COPY THE IMAGEApproximately how many drinks would a 100 -lb person have consumed in 1 hr to reach a blood-alcohol level of $0.08 \% ?$
Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count asone drink.CAN'T COPY THE IMAGEApproximately how many drinks would a 160 -lb person have consumed in 1 hr to reach a blood-alcohol level of $0.08 \% ?$
Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count asone drink.CAN'T COPY THE IMAGEWhat can you conclude about the weight of someone who has consumed 3 drinks in 1 hr without reaching a blood-alcohol level of $0.08 \% ?$
Driving under the Influence. A blood-alcohol level of $0.08 \%$ or higher makes driving illegal in the United States. This bar graph shows how many drinks a person of a certain weight would need to consume in I $\overline{h r}$ to achieve a blood-alcohol level of $0.08 \% .$ Note that a 12 -oz beer, a 5 -oz glass of wine, or a cocktail containing $1 \frac{1}{2}$ oz of distilled liquor all count asone drink.CAN'T COPY THE IMAGEWhat can you conclude about the weight of someone who has consumed 4 drinks in 1 hr without reaching a blood-alcohol level of $0.08 \% ?$
Use the information in Example 2 to answer Exercises $9-12$.In 2008 , there were $13,803,201$ full-time equivalent students in U.S. colleges and universities. What was the average federal loan per full-time equivalent student?
Use the information in Example 2 to answer Exercises $9-12$.In 2008 , there were $13,803,201$ full-time equivalent students in U.S. colleges and universities. What was the average education tax benefit received per fulltime equivalent student?
Use the information in Example 2 to answer Exercises $9-12$.Approximately $70 \%$ of state grants are need-based. How much did students receive in 2008 in need-based state grants?
Use the information in Example 2 to answer Exercises $9-12$.Approximately $19 \%$ of Pell grant dollars is given to students in for-profit institutions. How much did students in for-profit institutions receive in Pell grants in $2008 ?$
Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.CAN'T COPY THE CHARTIn $2007,$ Americans generated 254 million tons of waste. How much of the waste was glass?
Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.In 2007 , the average American generated 4.62 lb of waste per day. How much of that was paper?
Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.CAN'T COPY THE CHARTAmericans are recycling about $23.7 \%$ of all glass that is in the waste stream. How much glass did Americans recycle in $2007 ? \text { (See Exercise } 13 .)$
Sorting Solid Waste. Use the pie chart below to answer Exercises $13-16$.CAN'T COPY THE CHARTAmericans are recycling about $54.5 \%$ of all paper. What amount of paper did the average American recycle per day in $2007 ?$ (Use the information in Exercise $14 .)$
The graph below shows the number of U.S. households with only wireless phones.CAN'T COPY THE IMAGEApproximately how many households were wireless only in $2005 ?$
The graph below shows the number of U.S. households with only wireless phones.CAN'T COPY THE IMAGEApproximately how many households were wireless only in $2008 ?$
The graph below shows the number of U.S. households with only wireless phones.CAN'T COPY THE IMAGE
The graph below shows the number of U.S. households with only wireless phones.CAN'T COPY THE IMAGEBy how much did the number of wireless-only households increase from 2005 to $2006 ?$
Plot each group of points.$$(1,2),(-2,3),(4,-1),(-5,-3),(4,0),(0,-2)$$
Plot each group of points.$$(-2,-4),(4,-3),(5,4),(-1,0),(-4,4),(0,5)$$
Plot each group of points.$$\begin{aligned}&(4,4),(-2,4),(5,-3),(-5,-5),(0,4),(0,-4)\\&(3,0),(-4,0)\end{aligned}$$
Plot each group of points.$$\begin{aligned}&(2,5),(-1,3),(3,-2),(-2,-4),(0,4),(0,-5)\\&(5,0),(-5,0)\end{aligned}$$
Listed below are estimates of the number of text messages sent in the United States. Make a line graph of the data.CAN'T COPY THE GRAPH
Make a line graph of the data in the table below, listing years on the horizontal scale.CAN'T COPY THE GRAPH
In Exercises $27-30,$ find the coordinates of points $A, B, C$ $D,$ and $E$.CAN'T COPY THE GRAPH
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(-75,5),(-18,-2),(9,-4)$$
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(-13,3),(48,-1),(62,-4)$$
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(-1,83),(-5,-14),(5,37)$$
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(2,-79),(4,-25),(-4,12)$$
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(-10,-4),(-16,7),(3,15)$$
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(5,-16),(-7,-4),(12,3)$$
In Exercises $31-40,$ use a grid 10 squares wide and 10 squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.(-100,-5),(350,20),(800,37)
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(750,-8),(-150,17),(400,32)$$
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(-83,491),(-124,-95),(54,-238)$$
In Exercises $31-40,$ use a grid 10 squares wide and IO squares high to plot the given coordinates. Choose your scale carefully. Scales may vary.$$(738,-89),(-49,-6),(-165,53)$$
In which quadrant or on which axis is each point located?$$(7,-2)$$
In which quadrant or on which axis is each point located?$$(-1,-4)$$
In which quadrant or on which axis is each point located?$$(-4,-3)$$
In which quadrant or on which axis is each point located?$$(1,-5)$$
In which quadrant or on which axis is each point located?$$(0,-3)$$
In which quadrant or on which axis is each point located?$$(6,0)$$
In which quadrant or on which axis is each point located?$$(-4.9,8.3)$$
In which quadrant or on which axis is each point located?$$(7.5,2.9)$$
In which quadrant or on which axis is each point located?$$\left(-\frac{5}{2}, 0\right)$$
In which quadrant or on which axis is each point located?$$(0,2.8)$$
In which quadrant or on which axis is each point located?$$(160,2)$$
In which quadrant or on which axis is each point located?$$\left(-\frac{1}{2}, 2000\right)$$
In which quadrants are the first coordinates positive?
In which quadrants are the second coordinates negative?
In which quadrants do both coordinates have the same sign?
In which quadrants do the first and second coordinates have opposite signs?
For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.$$[-3,15,-50,500]$$
For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.$$[-8000,0,-100,600]$$
For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.$$\left[-\frac{1}{2}, 1,0,0.1\right]$$
For Exercises $57-60,$ set up the indicated viewing window on a graphing calculator, choosing appropriate scales for the axes. Choice of scale may vary.$$\left[-2.6,2.6,-\frac{1}{4}, \frac{1}{4}\right]$$
The graph below was included in a mailing sent by Agway $^{\mathscr{Q}}$ to their oil customers in 2000 . What information is missing from the graph and why is the graph misleading?CAN'T COPY THE GRAPH
What do all of the points on the vertical axis of a graph have in common?
To prepare for Section 3.2 , review solving for a variable (Section 2.3).$5 y=2 x$
To prepare for Section 3.2 , review solving for a variable (Section 2.3).$$2 y=-3 x$$
To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$$$x-y=8$$
To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$$$2 x+5 y=10$$
To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$$$2 x+3 y=5$$
To prepare for Section $3.2,$ review solving for a variable $(\text {Section } 2.3)$$$5 x-8 y=1$$
Describe what the result would be if the first and second coordinates of every point in the following graph of an arrow were interchanged.CAN'T COPY THE GRAPH
The graph accompanying Example 3 flattens out. Why do you think this occurs?
In which quadrant(s) could a point be located if its coordinates are opposites of each other?
In which quadrant(s) could a point be located if its coordinates are reciprocals of each other?
The points $(-1,1),(4,1),$ and $(4,-5)$ are three vertices of a rectangle. Find the coordinates of the fourth vertex.
The pairs $(-2,-3),(-1,2),$ and $(4,-3)$ can serve as three (of four) vertices for three different parallelograms. Find the fourth vertex of each parallelogram.
Graph eight points such that the sum of the coordinates in each pair is $7 .$ Answers may vary.
Find the perimeter of a rectangle if three of its vertices are $(5,-2),(-3,-2),$ and $(-3,3)$
Find the area of a triangle whose vertices have coordinates $(0,9),(0,-4),$ and $(5,-4)$
Coordinates can also be used to describe the location on a sphere: 0" latitude is the equator and 0' longitude is a line from the North Pole to the South Pole through France and Algeria. In the figure shown here, hurricane Clara is at a point about 260 mi northwest of Bermuda near latitude $36.0^{\circ}$ North, longitude 69.0^{\circ} West.CAN'T COPY THE IMAGEApproximate the latitude and the longitude of Bermuda.
Coordinates can also be used to describe the location on a sphere: 0" latitude is the equator and 0' longitude is a line from the North Pole to the South Pole through France and Algeria. In the figure shown here, hurricane Clara is at a point about 260 mi northwest of Bermuda near latitude $36.0^{\circ}$ North, longitude 69.0^{\circ} West.CAN'T COPY THE IMAGEApproximate the latitude and the longitude of Lake Okeechobee.
In the Star Trek science-fiction series, a threedimensional coordinate system is used to locate objects in space. If the center of a planet is used as the origin, how many "quadrants" will exist? Why? If possible, sketch a three-dimensional coordinate system and label each "quadrant"