Prealgebra and Introductory Algebra

Richard N. Aufmann, Joanne S. Lockwood

Chapter 12 Linear Equations in Two Variables - all with Video Answers

Educators

Section 1

The Rectangular Coordinate System

00:14

Problem 1

In which quadrant is the graph of $(-3,4)$ located?

Charles Carter

Numerade Educator

00:12

Problem 2

In which quadrant is the graph of $(2,-5)$ located?

Charles Carter

Numerade Educator

00:13

Problem 3

On which axis does the graph of $(0,-4)$ lie?

Charles Carter

Numerade Educator

00:17

Problem 4

On which axis does the graph of $(-6,0)$ lie?

Charles Carter

Numerade Educator

00:52

Problem 5

Name any two points on a horizontal line that is 2 units above the $x$ -axis.

Christy Galilei

Numerade Educator

00:23

Problem 6

Name any two points on a vertical line that is 3 units to the right of the $y$ -axis.

Charles Carter

Numerade Educator

00:25

Problem 7

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
To graph the point (5, -4) , start at the origin and move 5 units _____ and 4 units _____.

Charles Carter

Numerade Educator

00:22

Problem 8

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
To graph the point $(-1,7),$ start at the origin and move 1 unit _____ and 7 units _____.

Charles Carter

Numerade Educator

00:16

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
Write as an ordered pair the coordinates of the point whose $x$ -coordinate is 6 and whose $y$ -coordinate is $-5$.

Charles Carter

Numerade Educator

00:14

Problem 10

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
Write as an ordered pair the coordinates of the point whose $y$ -coordinate is 8 and whose $x$ -coordinate is $-7$

Charles Carter

Numerade Educator

00:34

Problem 11

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
To decide whether the ordered pair (1, 7) is a solution of the equation $y = 2x + 5$,
substitute 1 for _____ and 7 for _____ to see whether the ordered pair (1, 7) makes the equation
$y=2 x+5$ a true statement.

Charles Carter

Numerade Educator

00:23

Problem 12

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
The graphs of $y=\frac{1}{4} x-6$ and $f(x)=$_____ are identical.

Charles Carter

Numerade Educator

00:31

Problem 13

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
A relation is a set of _____. The set of first coordinates of the ordered pairs is called the _____
of the relation. The set of second coordinates is called the _____ of the relation.

Charles Carter

Numerade Educator

00:31

Problem 14

Complete Exercises 7 and 8 by filling in each blank with the word left , right, up, or down.
The symbol $f(x)$ is read "f_____ $x$ "or "the value of $f$ _____ $x$ " It is a symbol for the number that the function $f$ pairs with _____.

Charles Carter

Numerade Educator

00:37

Problem 15

Graph $(-2,1),(3,-5)$ $(-2,4),$ and $(0,3)$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:31

Problem 16

Graph $(5,-1),(-3,-3)$ $(-1,0),$ and $(1,-1)$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:26

Problem 17

Graph $(0,0),(0,-5)$ $(-3,0),$ and $(0,2)$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:28

Problem 18

Graph $(-4,5),(-3,1)$ $(3,-4),$ and $(5,0)$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:27

Problem 19

Graph $(-1,4),(-2,-3)$ $(0,2),$ and $(4,0)$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:27

Problem 20

Graph $(5,2),(-4,-1)$ $(0,0),$ and $(0,3)$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:39

Problem 21

Find the coordinates of each of the points.
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:41

Problem 22

Find the coordinates of each of the points.
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:40

Problem 23

Find the coordinates of each of the points.
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:37

Problem 24

Find the coordinates of each of the points.
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:48

Problem 25

a. Name the abscissas of points $A$ and $C$.
b. Name the ordinates of points $B$ and $D$.
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:36

Problem 26

a. Name the abscissas of points $A$ and $C$.
b. Name the ordinates of points $B$ and $D$.
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:57

Problem 27

Let $a$ and $b$ be positive numbers such that $a<b$. In which quadrant is each point located?
a. $(a, b)$
b. $(-a, b)$
c. $(b-a,-b)$
d. $(a-b,-b-a)$

Charles Carter

Numerade Educator

00:58

Problem 28

Let $a$ and $b$ be positive numbers. State whether the two given points lie on the $x$ -axis, the $y$ -axis, a horizontal line other than the $x$ -axis, or a vertical line other than the $y$ -axis.
a. $(-a, b)$ and $(-a, 0)$
b. $(a, 0)$ and $(-b, 0)$

Charles Carter

Numerade Educator

00:20

Problem 29

Is $(3,4)$ a solution of $y=-x+7 ?$

Charles Carter

Numerade Educator

00:20

Problem 30

Is $(2,-3)$ a solution of $y=x+5 ?$

Charles Carter

Numerade Educator

00:32

Problem 31

Is $(-1,2)$ a solution of $y=\frac{1}{2} x-1 ?$

Charles Carter

Numerade Educator

00:22

Problem 32

Is $(1,-3)$ a solution of $y=-2 x-1 ?$

Charles Carter

Numerade Educator

00:28

Problem 33

Is $(4,1)$ a solution of $2 x-5 y=4 ?$

Charles Carter

Numerade Educator

00:33

Problem 34

Is $(-5,3)$ a solution of $3 x-2 y=9 ?$

Charles Carter

Numerade Educator

01:03

Problem 35

Suppose $(x, y)$ is a solution of the equation $y=-3 x+6,$ where $x>2 .$ Is $y$ positive or negative?

Charles Carter

Numerade Educator

01:17

Problem 36

Suppose $(x, y)$ is a solution of the equation $y=4 x-8,$ where $y>0 .$ Is $x$ less than or greater than $2 ?$

Charles Carter

Numerade Educator

00:29

Problem 37

Graph the ordered-pair solutions of the equation for the given values of $x .$
$$y=2 x ; x=-2,-1,0,2$$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:34

Problem 38

Graph the ordered-pair solutions of the equation for the given values of $x .$
$$y=-2 x ; x=-2,-1,0,2$$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:50

Problem 39

Graph the ordered-pair solutions of the equation for the given values of $x .$
$$y=\frac{2}{3} x+1 ; x=-3,0,3$$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:48

Problem 40

Graph the ordered-pair solutions of the equation for the given values of $x .$
$$y=-\frac{1}{3} x-2 ; x=-3,0,3$$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:56

Problem 41

Graph the ordered-pair solutions of the equation for the given values of $x .$
$$2 x+3 y=6 ; x=-3,0,3$$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

01:16

Problem 42

Graph the ordered-pair solutions of the equation for the given values of $x .$
$$x-2 y=4 ; x=-2,0,2$$
CAN'T COPY THE GRAPH

Charles Carter

Numerade Educator

00:51

Problem 43

A relation has domain $A$ and range $B$. Each ordered pair in the relation is of the form (date, person born on that date). Is this relation a function?

Charles Carter

Numerade Educator

00:31

Problem 44

A relation has domain $B$ and range $A$. Each ordered pair in the relation is of the form (person, birth date of that person). Is this relation a function?

Charles Carter

Numerade Educator

01:53

Problem 45

See the news clipping at the right. The table below shows the ages and finishing times of the top eight finishers in the Manhattan Island Swim. Write a relation in which the first coordinate is the age of a swimmer and the second coordinate is the swimmer's finishing time. Is the relation a function?
CAN'T COPY THE TABLE

Charles Carter

Numerade Educator

00:54

Problem 46

The table below shows the number of Calories a 150 -pound person burns in 1 h while running at various speeds, in miles per hour. Write a relation in which the first coordinate is the speed of the runner and the second coordinate is the number of Calories burned. Is the relation a function?
CAN'T COPY THE TABLE

Charles Carter

Numerade Educator

01:12

Problem 47

The table at the right shows the U.S. Department of Agriculture's recommended limits on saturated fat intake, in grams. Write a relation in which the first coordinate is a person's daily Calorie intake and the second coordinate is the recommended limit on saturated fat intake. Is the relation a function?
CAN'T COPY THE TABLE

Charles Carter

Numerade Educator

01:52

Problem 48

The table at the right shows the birth rates, in births per thousand people per year, and life expectancies, in years, for various countries. (Source: www.cia.gov) Write a relation in which the first coordinate is the birth rate and the second coordinate is the life expectancy. Is the relation a function?
CAN'T COPY THE TABLE

Charles Carter

Numerade Educator

00:30

Problem 49

Find the domain and range of the relation. State whether or not the relation is a function.
$$\{(0,0),(2,0),(4,0),(6,0)\}$$

Charles Carter

Numerade Educator

00:41

Problem 50

Find the domain and range of the relation. State whether or not the relation is a function.
$$\{(-2,2),(0,2),(1,2),(2,2)\}$$

Charles Carter

Numerade Educator

00:43

Problem 51

Find the domain and range of the relation. State whether or not the relation is a function.
$$\{(2,2),(2,4),(2,6),(2,8)\}$$

Charles Carter

Numerade Educator

00:50

Problem 52

Find the domain and range of the relation. State whether or not the relation is a function.
$$\{(-4,4),(-2,2),(0,0),(-2,-2)\}$$

Charles Carter

Numerade Educator

01:13

Problem 53

Does $y=2 x+3,$ where $x \in\{-2,-1,1,4\},$ define $y$ as a function of $x ?$

Charles Carter

Numerade Educator

00:55

Problem 54

Does $|y|=x-1,$ where $x \in\{1,2,3,4\},$ define $y$ as a function of $x ?$

Charles Carter

Numerade Educator

00:46

Problem 55

Does $y=x^{2},$ where $x \in\{-2,-1,0,1,2\},$ define $y$ as a function of $x ?$

Charles Carter

Numerade Educator

00:22

Problem 56

Evaluate a function.
Given $f(x)=3 x-4,$ find $f(4)$

Charles Carter

Numerade Educator

00:25

Problem 57

Evaluate a function.
Given $f(x)=5 x+1,$ find $f(2)$.

Charles Carter

Numerade Educator

00:19

Problem 58

Evaluate a function.
Given $f(x)=x^{2},$ find $f(3)$.

Charles Carter

Numerade Educator

00:30

Problem 59

Evaluate a function.
Given $f(x)=x^{2}-1,$ find $f(1)$.

Charles Carter

Numerade Educator

00:36

Problem 60

Evaluate a function.
Given $G(x)=x^{2}+x,$ find $G(-2)$.

Charles Carter

Numerade Educator

00:34

Problem 61

Evaluate a function.
Given $H(x)=x^{2}-x,$ find $H(-2)$.

Charles Carter

Numerade Educator

00:31

Problem 62

Evaluate a function.
Given $s(t)=\frac{3}{t-1},$ find $s(-2)$.

Charles Carter

Numerade Educator

00:42

Problem 63

Evaluate a function.
Given $P(x)=\frac{4}{2 x+1},$ find $P(-2)$.

Charles Carter

Numerade Educator

00:50

Problem 64

Evaluate a function.
Given $h(x)=3 x^{2}-2 x+1,$ find $h(3)$.

Charles Carter

Numerade Educator

00:38

Problem 65

Evaluate a function.
Given $Q(r)=4 r^{2}-r-3,$ find $Q(2)$.

Charles Carter

Numerade Educator

00:39

Problem 66

Evaluate a function.
Given $f(x)=\frac{x}{x+5},$ find $f(-3)$.

Charles Carter

Numerade Educator

00:36

Problem 67

Evaluate a function.
Given $v(t)=\frac{2 t}{2 t+1},$ find $v(3)$.

Charles Carter

Numerade Educator

00:45

Problem 68

Use the function $f(x)=x^{2}-4 .$ For the given condition on $a$ determine whether $f(a)$ must be positive, must be negative, or could be either positive or negative.
$$a>2$$

Charles Carter

Numerade Educator

01:09

Problem 69

Use the function $f(x)=x^{2}-4 .$ For the given condition on $a$ determine whether $f(a)$ must be positive, must be negative, or could be either positive or negative.
$$a<0$$

Charles Carter

Numerade Educator

01:10

Problem 70

Use the function $f(x)=x^{2}-4 .$ For the given condition on $a$ determine whether $f(a)$ must be positive, must be negative, or could be either positive or negative.
$$a>-2$$

Charles Carter

Numerade Educator

00:33

Problem 71

Use the function $f(x)=x^{2}-4 .$ For the given condition on $a$ determine whether $f(a)$ must be positive, must be negative, or could be either positive or negative.
$$a<-2$$

Charles Carter

Numerade Educator

00:15

Problem 72

Find the distance from the given point to the horizontal axis.
$$(-5,1)$$

Charles Carter

Numerade Educator

00:26

Problem 73

Find the distance from the given point to the horizontal axis.
$$(3,-4)$$

Charles Carter

Numerade Educator

00:14

Problem 74

Find the distance from the given point to the horizontal axis.
$$(-6,0)$$

Charles Carter

Numerade Educator

00:23

Problem 75

Find the distance from the given point to the vertical axis.
$$(-2,4)$$

Charles Carter

Numerade Educator

00:14

Problem 76

Find the distance from the given point to the vertical axis.
$$(1,-3)$$

Charles Carter

Numerade Educator

00:14

Problem 77

Find the distance from the given point to the vertical axis.
$$(5,0)$$

Charles Carter

Numerade Educator

00:12

Problem 78

Name the coordinates of a point plotted at the origin of the rectangular coordinate system.

Charles Carter

Numerade Educator

01:02

Problem 79

Write a paragraph explaining how to plot points in a rectangular coordinate system.

Charles Carter

Numerade Educator

01:51

Problem 80

Functions are a part of our everyday lives. For example, the cost to mail a package via first-class mail is a function of the weight of the package. The tuition paid by a part-time student is a function of the number of credit hours the student registers for. Provide other examples of functions.

Charles Carter

Numerade Educator

01:33

Problem 81

Define three situations that describe relations that are not functions. One example is the set of ordered pairs in which the first coordinates are the runs scored by a baseball team and the second coordinates are either W for a win or L for a loss.

Charles Carter

Numerade Educator

01:37

Problem 82

There is an imaginary coordinate system on Earth that consists of longitude and latitude. Write a report on how location is determined on the surface of Earth.

Charles Carter

Numerade Educator

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