Elementary and Intermediate Algebra 5th

Alan S. Tussy, R. David Gustafson

Chapter 3 Graphing Linear Equations and Inequalities in Two Variables; Functions - all with Video Answers

Educators

Section 1

Graphing Using the Rectangular Coordinate System

00:29

Problem 1

Fill in the blanks.
$(7,1)$ is called an __pair.

Eva R.

Numerade Educator

00:35

Problem 2

Fill in the blanks.
In the ordered pair $(2,-5),$ the -coordinate is 2 and the
$y=$
is $-5$

Eva R.

Numerade Educator

00:32

Problem 3

Fill in the blanks.
A rectangular coordinate system is formed by two perpendicular number lines called the $x$ - __and the $y=__The point where the axes cross is called the ___

Eva R.

Numerade Educator

00:46

Problem 4

Fill in the blanks.
The $x$ - and $y$ -axes divide the coordinate plane into four regions called ___.

Eva R.

Numerade Educator

00:34

Problem 5

Fill in the blanks.
The point with coordinates $(4,2)$ can be graphed on a
___coordinate system.

Eva R.

Numerade Educator

00:24

Problem 6

Fill in the blanks.
The process of locating the position of a point on a coordinate plane is called __ the point.

Eva R.

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01:32

Fill in the blanks.
a. To plot $(-5,4),$ we start at the ___and move 5 units to the ___ and then move 4 units___.
b. To plot $\left(6,-\frac{3}{2}\right),$ we start at the___ and move 6 units to the___ and then move $\frac{3}{2}$ units___.

Eva R.

Numerade Educator

02:32

Problem 8

Fill in the blanks.
In which quadrant is each point located?
a. $(-2,7)$
b. $\left(\frac{1}{2}, \frac{15}{16}\right)$
c. $(-1,-2.75)$
d. $(50,-16)$

Eva R.

Numerade Educator

02:36

Problem 9

Fill in the blanks.
a. In which quadrants are the second coordinates of points positive?
b. In which quadrants are the first coordinates of points negative?
c. In which quadrant do points with a positive $x$ -coordinate and a negative $y$ -coordinate lie?
d. On what axis are the first coordinates of points zero?

Eva R.

Numerade Educator

03:28

Problem 10

The number of bushels of wheat produced per acre depends on the amount of water it receives. Plot the data in the table as ordered pairs and draw a straight line through the points. Use the graph to determine how many bushels per acre will be produced if
a. 6 inches of rain fall.
b. 10 inches of rain fall.
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:09

Problem 11

Explain the difference between $(3,5)$ and (3 5)

Eva R.

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00:53

Problem 12

In a paired-data table, does the first or second column contain values associated with the vertical axis of a graph?

Eva R.

Numerade Educator

01:31

Problem 13

Do these ordered pairs name the same point?
$$
\left(2.5,-\frac{7}{2}\right),\left(2 \frac{1}{2},-3.5\right),\left(2.5,-3 \frac{1}{2}\right)
$$

Eva R.

Numerade Educator

00:57

Problem 14

$\mathrm{Do}(3,2)$ and $(2,3)$ represent the same point?

Eva R.

Numerade Educator

00:35

Problem 15

In the ordered pair $(4,5),$ is the number 4 associated with the horizontal or the vertical axis?

Eva R.

Numerade Educator

00:40

Problem 16

Fill in the blank: In the notation $P(4,5),$ the capital letter $P$ is used to name a ___.

Eva R.

Numerade Educator

02:43

Problem 17

Plot each point:
$(-3,4),(4,3.5),\left(-2,-\frac{5}{2}\right),(0,-4),\left(\frac{3}{2}, 0\right),(2.7,-4.1)$

Eva R.

Numerade Educator

02:26

Problem 18

Plot each point:
$(4,4),(0.5,-3),(-3.9,-3.2),(0,-1),(0,0),(0,3),(-2,0)$

Eva R.

Numerade Educator

02:15

Problem 19

Complete the coordinates for each point in figure (a) below.
(GRAPH CANNOT COPY)

Eva R.

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02:08

Problem 20

Find the coordinates of points $A, B, C, D, E,$ and $F$ in figure (b) above.
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:07

Problem 21

The following graph gives the heart rate of a woman before, during, and after an aerobic workout.
a. What was her heart rate before beginning the workout?
b. After beginning her workout, how long did it take the woman to reach her training-zone heart rate?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:39

Problem 22

The following graph gives the heart rate of a woman before, during, and after an aerobic workout.
a. What was the woman's heart rate half un hour after beginning the workout"?
b. For how long did the woman work out at her training zone?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:48

Problem 23

The following graph gives the heart rate of a woman before, during, and after an aerobic workout.
a. $\Lambda t$ what time was her heart rate 100 beats per minute?
b. How long was her cool-down period?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

02:28

Problem 24

The following graph gives the heart rate of a woman before, during, and after an aerobic workout.
a. What was the difference in the woman's heart rate before the workout and after the cool-down period?
b. What was her approximate heart rate 8 minutes after beginning?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:24

Problem 25

The following graph shows the depths of a submarine at certain times after it leaves port.
a. For how long does the sub travel at sea level?
b. What is the depth of the sub 5 hours after leaving port?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:02

Problem 26

The following graph shows the depths of a submarine at certain times after it leaves port.
a. Once the sub begins to dive, how long does it take to reach $-1,000$ ficet in depth?
b. For how long does the sub travel at a depth of $1,000$ foct?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:12

Problem 27

The following graph shows the depths of a submarine at certain times after it leaves port.
a. Explain what happens 6 hours after the sub leaves port.
b. What is the depth of the sub 8 hours after leaving port?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

02:01

Problem 28

The following graph shows the depths of a submarine at certain times after it leaves port.
a. How long does it take the sub to first reach $-500$ feet in depth?
b. Approximate the time when the sub reaches $-500$ feet in depth for the second time.
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

03:25

Problem 29

Find the coordinates of each rivet, weld, and anchor.
(FIGURE CANNOT COPY)

Eva R.

Numerade Educator

01:48

Problem 30

$\Lambda$ golfer is videotaped and then has her swing displayed on a computer monitor so that it can be analyzed. Give the coordinates of the three highlighted puints in red.
(FIGURE CANNOT COPY)

Eva R.

Numerade Educator

01:17

Problem 31

In the game Battleship, players use coordinates to drop depth charges from their ships to hit submarines, What coordinates should be used to make three hits on the submarine seen here? Express each answer in the form (letter, number).
(FIGURE CANNOT COPY)

Eva R.

Numerade Educator

03:59

Problem 32

Use coordinates of the form (number, letter) to locate cach of the following on the map: Tempe, Glendalc, Paradise Valley, Sky Harbor Airport, and the intersection of Camelback
(FIGURE CANNOT COPY)

Eva R.

Numerade Educator

01:57

Problem 33

Dentists describe tecth as being located in one of four quadrants as shown above.
a. How many teeth are in each quadrant?
b. Why would the upper left quadrant appear on the right in the illustration?
(FIGURE CANNOT COPY)

Eva R.

Numerade Educator

02:13

Problem 34

A coordinate system that describes the location of any place on the surface of the Earth uses a series of latitude and longitude lines, as shown below. Estimate the location of the Deep Water Horizon (the oil drilling rig in the Gulf of Mexico that exploded in 2010 ) using an ordered pair of the form (latitude, longitude). (Source; sailwx.info)
(FIGURE CANNOT COPY)

Eva R.

Numerade Educator

01:51

Problem 35

The graphs show how the path of a stream of water changes when the hose is held at two different angles.
a. At which angle does the stream of water shoot up higher? How much higher?
b. At which angle does the stream of water shoot out farther? How much farther?
(GRAPH CANNOT COPY)

Eva R.

Numerade Educator

01:53

Problem 36

Three vertices (corners) of a rectangle are $(2,1),(6,1)$ and $(6,4) .$ Find the coordinates of the fourth vertex. Then find the area of the rectangle.

Eva R.

Numerade Educator

02:11

Problem 37

Three vertices (corners) of a right triangle are $(-1,-7),(-5,-7),$ and $(-5,-2) .$ Find the area of the triangle.

Eva R.

Numerade Educator

06:22

Problem 38

A scale model of the block letter $\mathrm{H}$ in the Hollywood sign can be drawn by plotting the following points and connecting them: $(0,0),(13,0),(13,16),(26,16),(26,0)$ $(39,0),(39,45),(26,45),(26,29),(13,29),(13,45),$ and
$(0,45) .$ The scale is 1 unit on the graph is equal to 1 foot on the actual sign. If a gallon of paint covers 350 square feet, how many gallons are needed to paint the front side of the letter H? Round to the nearest gallon.
(FIGURE CANNOT COPY)

Eva R.

Numerade Educator

02:39

Problem 39

The table below shows the number of miles that an 18-wheel truck can be driven on a given number of gallons of diesel fuel. Plot the data in the table as ordered pairs. Then draw a straight line through the points.
a. How far can the truck go on 4 gallons of fuel?
b. How many gallons of fuel are needed to travel a distance of
30 miles?
c. How far can the truck go on 7 gallons of fuel?
(TABLE CANNOT COPY)

Eva R.

Numerade Educator

02:10

Problem 40

The table below shows the cost to rent a sailboat for
a given number of hours. Plot the data in the table as ordered pairs. Then draw a straight line through the points.
a. What does it cost to rent the boat for 3 hours?
b. For how long can the boat be rented for $\$ 60 ?$
c. What does it cost to rent the boat for 9 hours?
(TABLE CANNOT COPY)

Eva R.

Numerade Educator

03:14

Problem 41

The table below shows the value (in thousands of dollars) of a color copier at various lengths of time after its purchase. Plot the data in the table as ordered pairs. Then draw a straight line passing through the points.
a. What does the point $(3,7)$ on the graph tell you?
b. Find the value of the copier when it is 7 years old.
c. After how many years will the copier be worth $\$ 2,500 ?$
(TABLE CANNOT COPY)

Eva R.

Numerade Educator

02:43

Problem 42

The table below shows the number of people at a public swimming pool at various times during the day. (O represents noon, 1 represents $1 \mathrm{m}$, and so on. ) Plot the data in the table as ordered pairs. Then draw a straight line passing through the points.
a. How many people will be at the pool at 6 RM.?
b. At what time will there be 250 pcople at the pool?
c. At what time will the number of people at the pool be half of what it was at noon?
(TABLE CANNOT COPY)

Eva R.

Numerade Educator

00:51

Problem 43

Explain why the point $(-3,3)$ is not the same as the point
$(3,-3)$

Eva R.

Numerade Educator

01:34

Problem 44

Explain how to plot the point $(-2,5)$

Eva R.

Numerade Educator

01:29

Problem 45

Use the Internet to perform a search of the name René Descartes. After reading about him, explain how a fly on his bedroom ceiling provided the inspiration for the concept of a rectangular coordinate system.

Eva R.

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01:22

Problem 46

Explain this diagram.
(DIAGRAM CANNOT COPY)

Eva R.

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01:26

Problem 47

Solve $A C=\frac{2}{3} h-T$ for $h$

Eva R.

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02:08

Problem 48

Solve $5(x+1) \leq 2(x-3) .$ Write the solution set in interval notation and graph it.

Eva R.

Numerade Educator

02:21

Problem 49

Evaluate: $\frac{-4(4+2)-2^{3}}{|-12-4(5)|}$

Eva R.

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01:02

Problem 50

Simplify:$\frac{24}{54}$

Eva R.

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01:37

Problem 51

In what quadrant does a point lie if the sum of its coordinates is negative and the product of its coordinates is positive?

Eva R.

Numerade Educator

01:41

Problem 52

Draw line segment $\overline{A B}$ with endpoints $A(6,5)$ and $B(-4,5)$ Suppose that the $x$ -coordinate of a point $C$ is the average of the $x$ -coordinates of points $A$ and $B$, and the $y$ -coordinate of point $C$ is the average of the $y$ -coordinates of points $A$ and $B$. Find the coordinates of point $C .$ Why is $C$ called the midpoint of $A B ?$

Eva R.

Numerade Educator