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Beginning & Intermediate Algebra

Elayn Martin-Gay

Chapter 8

More on Functions and Graphs - all with Video Answers

Educators

Section 1

Graphing and Writing Linear Functions

00:33

Problem 1

Graph each linear function. See Examples 1 and 2.
$f(x)=-2 x$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:32

Problem 2

Graph each linear function. See Examples 1 and 2.
$f(x)=2 x$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 3

Graph each linear function. See Examples 1 and 2.
$f(x)=-2 x+3$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:47

Problem 4

Graph each linear function. See Examples 1 and 2.
$f(x)=2 x+6$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:38

Problem 5

Graph each linear function. See Examples 1 and 2.
$f(x)=\frac{1}{2} x$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:36

Problem 6

Graph each linear function. See Examples 1 and 2.
$f(x)=\frac{1}{3} x$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:46

Problem 7

Graph each linear function. See Examples 1 and 2.
$f(x)=\frac{1}{2} x-4$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:36

Problem 8

Graph each linear function. See Examples 1 and 2.
$f(x)=\frac{1}{3} x-2$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 9

The graph of $f(x)=5 x$ follow. Use this graph to match each linear function with its graph. See Examples 1 and 2.
Graph can't copy
(a) Graph can't copy
(b) Graph can't copy
(c) Graph can't copy
(d) Graph can't copy

$f(x)=5 x-3$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:49

Problem 10

The graph of $f(x)=5 x$ follow. Use this graph to match each linear function with its graph. See Examples 1 and 2.
Graph can't copy
(a) Graph can't copy
(b) Graph can't copy
(c) Graph can't copy
(d) Graph can't copy

$f(x)=5 x-2$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:47

Problem 11

The graph of $f(x)=5 x$ follow. Use this graph to match each linear function with its graph. See Examples 1 and 2.
Graph can't copy
(a) Graph can't copy
(b) Graph can't copy
(c) Graph can't copy
(d) Graph can't copy

$f(x)=5 x+1$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 12

The graph of $f(x)=5 x$ follow. Use this graph to match each linear function with its graph. See Examples 1 and 2.
Graph can't copy
(a) Graph can't copy
(b) Graph can't copy
(c) Graph can't copy
(d) Graph can't copy

$f(x)=5 x+3$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:43

Problem 13

Use function notation to write the equation of each line with the given slope and $y$-intercept. See Example 3.
Slope $-1 ; y$-intercept $(0,1)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:37

Problem 14

Use function notation to write the equation of each line with the given slope and $y$-intercept. See Example 3.
Slope $\frac{1}{2} ; y$-intercept $(0,-6)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:34

Problem 15

Use function notation to write the equation of each line with the given slope and $y$-intercept. See Example 3.
Slope $2 ; y$-intercept $\left(0, \frac{3}{4}\right)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:35

Problem 16

Use function notation to write the equation of each line with the given slope and $y$-intercept. See Example 3.
Slope $-3 ; y$-intercept $\left(0,-\frac{1}{5}\right)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:34

Problem 17

Use function notation to write the equation of each line with the given slope and $y$-intercept. See Example 3.
Slope $\frac{2}{7} ; y$-intercept $(0,0)

Heather Zimmers
Heather Zimmers
Numerade Educator
00:37

Problem 18

Use function notation to write the equation of each line with the given slope and $y$-intercept. See Example 3.
Slope $-\frac{4}{5} ; y$-intercept $(0,0)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:42

Problem 19

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope 3 ; through $(1,2)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 20

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope 4 ; through $(5,1)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 21

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope -2 ; through $(1,-3)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:46

Problem 22

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope -4 ; through $(2,-4)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:52

Problem 23

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope $\frac{1}{2}$; through $(-6,2)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:51

Problem 24

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope $\frac{2}{3}$; through $(-9,4)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:49

Problem 25

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope $-\frac{9}{10}$; through $(-3,0)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:01

Problem 26

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. See Example 3.
Slope $-\frac{1}{5}$; through $(4,-6)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:49

Problem 27

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(2,0),(4,6)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:58

Problem 28

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(3,0),(7,8)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:15

Problem 29

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(-2,5),(-6,13)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:10

Problem 30

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(7,-4),(2,6)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:24

Problem 31

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(-2,-4),(-4,-3)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:17

Problem 32

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(-9,-2),(-3,10)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:21

Problem 33

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(-3,-8),(-6,-9)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:18

Problem 34

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$(8,-3),(4,-8)$

Heather Zimmers
Heather Zimmers
Numerade Educator
02:12

Problem 35

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$\left(\frac{3}{5}, \frac{2}{5}\right)$ and $\left(-\frac{1}{5}, \frac{7}{10}\right)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:25

Problem 36

Find an equation of the line passing through the given points. Use function notation to write the equation. See Example 4.
$\left(\frac{1}{2},-\frac{1}{4}\right)$ and $\left(\frac{3}{2}, \frac{3}{4}\right)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:55

Problem 37

Write an equation of each line using function notation. See Example 5.
Slope 0 ; through $(-2,-4)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 38

Write an equation of each line using function notation. See Example 5.
Horizontal; through $(-3,1)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:38

Problem 39

Write an equation of each line using function notation. See Example 5.
Horizontal; through $(0,5)$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:50

Problem 40

Write an equation of each line using function notation. See Example 5.
Slope 0 ; through $(-10,23)$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:11

Problem 41

Find an equation of each line. Write the equation using function notation. See Examples 6 and 7.
Through $(3,8)$; parallel to $f(x)=4 x-2$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:09

Problem 42

Find an equation of each line. Write the equation using function notation. See Examples 6 and 7.
Through $(1,5)$; parallel to $f(x)=3 x-4$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:35

Problem 43

Find an equation of each line. Write the equation using function notation. See Examples 6 and 7.
Through $(2,-5)$ perpendicular to $3 y=x-6$

Heather Zimmers
Heather Zimmers
Numerade Educator
02:01

Problem 44

Find an equation of each line. Write the equation using function notation. See Examples 6 and 7.
Through $(-4,8)$; perpendicular to $2 x-3 y=1$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:48

Problem 45

Find an equation of each line. Write the equation using function notation. See Examples 6 and 7.
Through $(-2,-3)$; parallel to $3 x+2 y=5$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:59

Problem 46

Find an equation of each line. Write the equation using function notation. See Examples 6 and 7.
Through $(-2,-3)$; perpendicular to $3 x+2 y=5$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:05

Problem 47

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Slope 2 ; through $(-2,3)$

Kyler Gray
Kyler Gray
Numerade Educator
01:03

Problem 48

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Slope 3; through $(-4,2)$

Kyler Gray
Kyler Gray
Numerade Educator
01:48

Problem 49

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(1,6)$ and $(5,2)$; use function notation

Kyler Gray
Kyler Gray
Numerade Educator
01:11

Problem 50

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(2,9)$ and $(8,6)$; use function notation

Heather Zimmers
Heather Zimmers
Numerade Educator
00:44

Problem 51

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
With slope $-\frac{1}{2} ; y$-intercept 11 ; use function notation

Heather Zimmers
Heather Zimmers
Numerade Educator
00:43

Problem 52

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
With slope $-4 ; y$-intercept $\frac{2}{9}$; use function notation

Heather Zimmers
Heather Zimmers
Numerade Educator
01:33

Problem 53

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(-7,-4)$ and $(0,-6)$

Kyler Gray
Kyler Gray
Numerade Educator
01:55

Problem 54

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(2,-8)$ and $(-4,-3)$

Kyler Gray
Kyler Gray
Numerade Educator
01:33

Problem 55

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Slope $-\frac{4}{3}$; through $(-5,0)$

Kyler Gray
Kyler Gray
Numerade Educator
00:48

Problem 56

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Slope $-\frac{3}{5}$; through $(4,-1)$

Erika Bustos
Erika Bustos
Numerade Educator
00:43

Problem 57

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Horizontal line; through $(-2,-10)$; use function notation

Heather Zimmers
Heather Zimmers
Numerade Educator
00:38

Problem 58

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Horizontal line; through $(1,0)$; use function notation

Heather Zimmers
Heather Zimmers
Numerade Educator
02:04

Problem 59

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(6,-2)$; parallel to the line $2 x+4 y=9$

Kyler Gray
Kyler Gray
Numerade Educator
01:49

Problem 60

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(8,-3)$; parallel to the line $6 x+2 y=5$

Kyler Gray
Kyler Gray
Numerade Educator
00:48

Problem 61

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Slope 0 ; through $(-9,12)$; use function notation

Heather Zimmers
Heather Zimmers
Numerade Educator
00:49

Problem 62

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Slope 0 ; through $(10,-8)$; use function notation

Heather Zimmers
Heather Zimmers
Numerade Educator
01:52

Problem 63

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(6,1)$; parallel to the line $8 x-y=9$

Kyler Gray
Kyler Gray
Numerade Educator
02:00

Problem 64

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(3,5)$; perpendicular to the line $2 x-y=8$

Kyler Gray
Kyler Gray
Numerade Educator
00:53

Problem 65

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(5,-6)$; perpendicular to $y=9$

Kyler Gray
Kyler Gray
Numerade Educator
00:57

Problem 66

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(-3,-5)$; parallel to $y=9$

Kyler Gray
Kyler Gray
Numerade Educator
02:00

Problem 67

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(2,-8)$ and $(-6,-5)$; use function notation

Kyler Gray
Kyler Gray
Numerade Educator
01:48

Problem 68

Find an equation of each line. Write the equation in standard form unless indicated otherwise. See Examples 3 through 7.
Through $(-4,-2)$ and $(-6,5)$; use function notation

Kyler Gray
Kyler Gray
Numerade Educator
01:55

Problem 69

From the Chapter 8 opener, we have two functions to describe the amount of sulfur dioxide emissions in the United States. For both functions, $x$ is the number of years since 1970 and $y$ (or $f(x)$ or $g(x))$ is the amount of emissions in millions of tons.
$$
f(x)=-0.59 x+32.38 \text { or } g(x)=-0.0045 x^2-0.37 x+30.89
$$

Use this for Exercises 69 through 74. See Section 3.6.
Find $f(30)$ and describe in words what this means.

Lili Schantz
Lili Schantz
Numerade Educator
01:55

Problem 70

From the Chapter 8 opener, we have two functions to describe the amount of sulfur dioxide emissions in the United States. For both functions, $x$ is the number of years since 1970 and $y$ (or $f(x)$ or $g(x))$ is the amount of emissions in millions of tons.
$$
f(x)=-0.59 x+32.38 \text { or } g(x)=-0.0045 x^2-0.37 x+30.89
$$

Use this for Exercises 69 through 74. See Section 3.6.
Find $g(30)$ and describe in words what this means.

Lili Schantz
Lili Schantz
Numerade Educator
01:55

Problem 71

From the Chapter 8 opener, we have two functions to describe the amount of sulfur dioxide emissions in the United States. For both functions, $x$ is the number of years since 1970 and $y$ (or $f(x)$ or $g(x))$ is the amount of emissions in millions of tons.
$$
f(x)=-0.59 x+32.38 \text { or } g(x)=-0.0045 x^2-0.37 x+30.89
$$

Use this for Exercises 69 through 74. See Section 3.6.
Find $f(50)$ and describe in words what this means.

Lili Schantz
Lili Schantz
Numerade Educator
01:55

Problem 72

From the Chapter 8 opener, we have two functions to describe the amount of sulfur dioxide emissions in the United States. For both functions, $x$ is the number of years since 1970 and $y$ (or $f(x)$ or $g(x))$ is the amount of emissions in millions of tons.
$$
f(x)=-0.59 x+32.38 \text { or } g(x)=-0.0045 x^2-0.37 x+30.89
$$

Use this for Exercises 69 through 74. See Section 3.6.
Find $g(50)$ and describe in words what this means.

Lili Schantz
Lili Schantz
Numerade Educator
01:55

Problem 73

From the Chapter 8 opener, we have two functions to describe the amount of sulfur dioxide emissions in the United States. For both functions, $x$ is the number of years since 1970 and $y$ (or $f(x)$ or $g(x))$ is the amount of emissions in millions of tons.
$$
f(x)=-0.59 x+32.38 \text { or } g(x)=-0.0045 x^2-0.37 x+30.89
$$

Use this for Exercises 69 through 74. See Section 3.6.
In 2000 , the actual level of sulfur dioxide emssions in the United States was 16 million tons. Use your results from Exercises 69 and 70 to decide which model, $f(x)$ or $g(x)$, provides a better estimate of the sulfur dioxide emissions for that year. Explain your answer.

Lili Schantz
Lili Schantz
Numerade Educator
01:55

Problem 74

From the Chapter 8 opener, we have two functions to describe the amount of sulfur dioxide emissions in the United States. For both functions, $x$ is the number of years since 1970 and $y$ (or $f(x)$ or $g(x))$ is the amount of emissions in millions of tons.
$$
f(x)=-0.59 x+32.38 \text { or } g(x)=-0.0045 x^2-0.37 x+30.89
$$

Use this for Exercises 69 through 74. See Section 3.6.
Assume the trends described in $f(x)$ and $g(x)$ continue. Find $f(60)$ and $g(60)$. Describe in words what each of these results means. Would you recommend using either model to predict sulfur dioxide emissions in the United States in the future? Explain your answer.

Lili Schantz
Lili Schantz
Numerade Educator
01:04

Problem 75

Find an equation of each line graphed. Write the equation using function notation. (Hint: Use each graph to write 2 ordered pair solutions. Find the slope of each line, then refer to Example 3 or $\mathbf{4}$ to complete.)
Graph can't copy

Heather Zimmers
Heather Zimmers
Numerade Educator
01:04

Problem 76

Find an equation of each line graphed. Write the equation using function notation. (Hint: Use each graph to write 2 ordered pair solutions. Find the slope of each line, then refer to Example 3 or $\mathbf{4}$ to complete.)
Graph can't copy

Heather Zimmers
Heather Zimmers
Numerade Educator
01:04

Problem 77

Find an equation of each line graphed. Write the equation using function notation. (Hint: Use each graph to write 2 ordered pair solutions. Find the slope of each line, then refer to Example 3 or $\mathbf{4}$ to complete.)
Graph can't copy

Heather Zimmers
Heather Zimmers
Numerade Educator
01:04

Problem 78

Find an equation of each line graphed. Write the equation using function notation. (Hint: Use each graph to write 2 ordered pair solutions. Find the slope of each line, then refer to Example 3 or $\mathbf{4}$ to complete.)
Graph can't copy

Heather Zimmers
Heather Zimmers
Numerade Educator
01:39

Problem 79

Solve.
A rock is dropped from the top of a 400 -foot building. After 1 second, the rock is traveling 32 feet per second. After 3 seconds, the rock is traveling 96 feet per second. Let $y$ be the rate of descent and $x$ be the number of seconds since the rock was dropped.
a. Write a linear equation that relates time $x$ to rate $y$. [Hint: Use the ordered pairs $(1,32)$ and $(3,96)$.]
b. Use this equation to determine the rate of travel of the rock 4 seconds after it was dropped.

Kyler Gray
Kyler Gray
Numerade Educator
03:23

Problem 80

Solve.
A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $$\$ 30,000$$. The anticipated profit for the end of the fourth year is $$\$ 66,000$$. The ratio of change in time to change in profit is constant. Let $x$ be years and $y$ be profit.
a. Write a linear equation that relates profit and time. [Hint: Use the ordered pairs $(1,30,000)$ and $(4,66,000)$.]
b. Use this equation to predict the company's profit at the end of the seventh year.
c. Predict when the profit should reach $$\$ 126,000$$.

Kyler Gray
Kyler Gray
Numerade Educator
02:23

Problem 81

Solve.
The Whammo Company has learned that by pricing a newly released flying disc at $$\$ 6$$, sales will reach 2000 per day. Raising the price to $$\$ 8$$ will cause the sales to fall to 1500 per day. Assume that the ratio of change in price to change in daily sales is constant and let $x$ be the price of the flying disc and $y$ be number of sales.
a. Find the linear equation that models the price-sales relationship for this flying disc. [Hint: The line must pass through $(6,2000)$ and $(8,1500)$.]
b. Use this equation to predict the daily sales of flying discs if the price is set at $$\$ 7.50$$.

Kyler Gray
Kyler Gray
Numerade Educator
02:19

Problem 82

Solve.
The Pool Fun Company has learned that by pricing a newly released pool noodle at $$\$ 3$$, sales will reach 10,000 pool noodles per day during the summer. Raising the price to $$\$ 5$$ will cause the sales to fall to 8000 pool noodles per day. Let $x$ be price and $y$ be the number sold.
a. Assume that the relationship between sales price and number of pool noodles sold is linear and write an equation describing this relationship. [Hint: The line must pass through $(3,10,000)$ and $(5,8000)$.]
b. Use this equation to predict the daily sales of pool noodles if the price is $$\$ 3.50$$.

Kyler Gray
Kyler Gray
Numerade Educator
02:01

Problem 83

Solve
The number of people employed in the United States as registered nurses was $3,080,100$ in 2020 . By 2030, this number is expected to rise to $3,356,800$. Let $y$ be the number of registered nurses employed in the United States in the year $x$, where $x=0$ represents 2020. (Source: U.S. Bureau of Labor Statistics)
a. Write a linear equation that models the number of people employed as registered nurses in year $x$.
b. Use this equation to estimate the number of people employed as registered nurses in 2028 .

Erika Bustos
Erika Bustos
Numerade Educator
06:54

Problem 84

Solve
In 2015, Target operated 1792 stores in the United States. By 2020, the number of stores had risen to 1897 . Let $y$ be the number of Target stores in the year $x$, where $x=0$ represents 2015. (Source: Target Corporation)
a. Write a linear equation that models the number of Target stores in year $x$.
b. Use this equation to predict the number of Target stores in 2026.

Noah Musser
Noah Musser
Numerade Educator
02:25

Problem 85

Solve
In 2015, the revenue from sales of music CDs in the United States was $$\$ 1521$$ million. By 2020 , this number had dropped to $$\$ 483$$ million. Let $y$ be the revenue (in millions of dollars) from sales of CDs in year $x$, where $x=0$ represents 2015. (Source: Recording Industry Association of America)
a. Write a linear equation that models the revenue (in millions of dollars) from sales of CDs in year $x$.
b. Use this equation to predict the revenue from sales of CDs in 2022.

Natalie Anderson
Natalie Anderson
Numerade Educator
01:39

Problem 86

Solve
The number of people employed in the United States as secretaries or administrative assistants was $3,363,900$ in 2020. By 2030, this number is expected to fall to $3,137,700$. Let $y$ be the number of secretaries or administrative assistants employed in the United States in the year $x$, where $x=0$ represents 2020 . (Source: U.S Bureau of Labor Statistics)
a. Write a linear equation that models the number of people employed as secretaries or administrative assistants in year $x$.
b. Use this equation to estimate the number of people employed as secretaries or administrative assistants in 2027.

Heather Zimmers
Heather Zimmers
Numerade Educator
03:35

Problem 87

Example:
Find an equation of the perpendicular bisector of the line seg. ment whose endpoints are $(2,6)$ and $(0,-2)$.
Graph can't copy
Solution:
A perpendicular bisector is a line that contains the midpoint of the given segment and is perpendicular to the segment.
Step 1. The midpoint of the segment with endpoints $(2,6)$ and $(0,-2)$ is $(1,2)$.
Step 2. The slope of the segment containing points $(2,6)$ and $(0,-2)$ is 4 .
Step 3. A line perpendicular to this line segment will have slope of $-\frac{1}{4}$.
Step 4. The equation of the line through the midpoint $(1,2)$ with a slope of $-\frac{1}{4}$ will be the equation of the perpendicular bisector. This equation in standard form is $x+4 y=9$.

Find an equation of the perpendicular bisector of the line segment whose endpoints are given. See the previous example.
$(3,-1) ;(-5,1)$

Heather Zimmers
Heather Zimmers
Numerade Educator
03:35

Problem 88

Example:
Find an equation of the perpendicular bisector of the line seg. ment whose endpoints are $(2,6)$ and $(0,-2)$.
Graph can't copy
Solution:
A perpendicular bisector is a line that contains the midpoint of the given segment and is perpendicular to the segment.
Step 1. The midpoint of the segment with endpoints $(2,6)$ and $(0,-2)$ is $(1,2)$.
Step 2. The slope of the segment containing points $(2,6)$ and $(0,-2)$ is 4 .
Step 3. A line perpendicular to this line segment will have slope of $-\frac{1}{4}$.
Step 4. The equation of the line through the midpoint $(1,2)$ with a slope of $-\frac{1}{4}$ will be the equation of the perpendicular bisector. This equation in standard form is $x+4 y=9$.

Find an equation of the perpendicular bisector of the line segment whose endpoints are given. See the previous example.
$(-6,-3) ;(-8,-1)$

Heather Zimmers
Heather Zimmers
Numerade Educator
03:35

Problem 89

Example:
Find an equation of the perpendicular bisector of the line seg. ment whose endpoints are $(2,6)$ and $(0,-2)$.
Graph can't copy
Solution:
A perpendicular bisector is a line that contains the midpoint of the given segment and is perpendicular to the segment.
Step 1. The midpoint of the segment with endpoints $(2,6)$ and $(0,-2)$ is $(1,2)$.
Step 2. The slope of the segment containing points $(2,6)$ and $(0,-2)$ is 4 .
Step 3. A line perpendicular to this line segment will have slope of $-\frac{1}{4}$.
Step 4. The equation of the line through the midpoint $(1,2)$ with a slope of $-\frac{1}{4}$ will be the equation of the perpendicular bisector. This equation in standard form is $x+4 y=9$.

Find an equation of the perpendicular bisector of the line segment whose endpoints are given. See the previous example.
$(-2,6) ;(-22,-4)$

Heather Zimmers
Heather Zimmers
Numerade Educator
03:35

Problem 90

Example:
Find an equation of the perpendicular bisector of the line seg. ment whose endpoints are $(2,6)$ and $(0,-2)$.
Graph can't copy
Solution:
A perpendicular bisector is a line that contains the midpoint of the given segment and is perpendicular to the segment.
Step 1. The midpoint of the segment with endpoints $(2,6)$ and $(0,-2)$ is $(1,2)$.
Step 2. The slope of the segment containing points $(2,6)$ and $(0,-2)$ is 4 .
Step 3. A line perpendicular to this line segment will have slope of $-\frac{1}{4}$.
Step 4. The equation of the line through the midpoint $(1,2)$ with a slope of $-\frac{1}{4}$ will be the equation of the perpendicular bisector. This equation in standard form is $x+4 y=9$.

Find an equation of the perpendicular bisector of the line segment whose endpoints are given. See the previous example.
$(5,8) ;(7,2)$

Heather Zimmers
Heather Zimmers
Numerade Educator
03:35

Problem 91

Example:
Find an equation of the perpendicular bisector of the line seg. ment whose endpoints are $(2,6)$ and $(0,-2)$.
Graph can't copy
Solution:
A perpendicular bisector is a line that contains the midpoint of the given segment and is perpendicular to the segment.
Step 1. The midpoint of the segment with endpoints $(2,6)$ and $(0,-2)$ is $(1,2)$.
Step 2. The slope of the segment containing points $(2,6)$ and $(0,-2)$ is 4 .
Step 3. A line perpendicular to this line segment will have slope of $-\frac{1}{4}$.
Step 4. The equation of the line through the midpoint $(1,2)$ with a slope of $-\frac{1}{4}$ will be the equation of the perpendicular bisector. This equation in standard form is $x+4 y=9$.

Find an equation of the perpendicular bisector of the line segment whose endpoints are given. See the previous example.
$(2,3) ;(-4,7)$

Heather Zimmers
Heather Zimmers
Numerade Educator
03:24

Problem 92

Example:
Find an equation of the perpendicular bisector of the line seg. ment whose endpoints are $(2,6)$ and $(0,-2)$.
Graph can't copy
Solution:
A perpendicular bisector is a line that contains the midpoint of the given segment and is perpendicular to the segment.
Step 1. The midpoint of the segment with endpoints $(2,6)$ and $(0,-2)$ is $(1,2)$.
Step 2. The slope of the segment containing points $(2,6)$ and $(0,-2)$ is 4 .
Step 3. A line perpendicular to this line segment will have slope of $-\frac{1}{4}$.
Step 4. The equation of the line through the midpoint $(1,2)$ with a slope of $-\frac{1}{4}$ will be the equation of the perpendicular bisector. This equation in standard form is $x+4 y=9$.

Find an equation of the perpendicular bisector of the line segment whose endpoints are given. See the previous example.
$(-6,8) ;(-4,-2)$

Heather Zimmers
Heather Zimmers
Numerade Educator
03:35

Problem 93

Example:
Find an equation of the perpendicular bisector of the line seg. ment whose endpoints are $(2,6)$ and $(0,-2)$.
Graph can't copy
Solution:
A perpendicular bisector is a line that contains the midpoint of the given segment and is perpendicular to the segment.
Step 1. The midpoint of the segment with endpoints $(2,6)$ and $(0,-2)$ is $(1,2)$.
Step 2. The slope of the segment containing points $(2,6)$ and $(0,-2)$ is 4 .
Step 3. A line perpendicular to this line segment will have slope of $-\frac{1}{4}$.
Step 4. The equation of the line through the midpoint $(1,2)$ with a slope of $-\frac{1}{4}$ will be the equation of the perpendicular bisector. This equation in standard form is $x+4 y=9$.

Find an equation of the perpendicular bisector of the line segment whose endpoints are given. See the previous example.
Describe how to check to see if the graph of $2 x-4 y=7$ passes through the points $(1.4,-1.05)$ and $(0,-1.75)$. Then follow your directions and check these points.

Heather Zimmers
Heather Zimmers
Numerade Educator