Algebra 1

Ron Larson, Laurie Boswell, Timothy D. Kanold

Chapter 5 Writing Linear Equations - all with Video Answers

Educators

Section 1

Writing Linear Equations in Slope-Intercept Form

01:08

Problem 1

Is 5 the $x$ -intercept or the $y$ -intercept of the line $y=3 x+5 ?$ Explain.

Nick Johnson

Numerade Educator

01:35

Problem 2

Describe the rate of change in the context of Example 3 on page 274 .

Nick Johnson

Numerade Educator

00:53

Problem 3

Write an equation of the line in slope-intercept form.
The slope is $1 ;$ the $y$ -intercept is $0 .$

Nick Johnson

Numerade Educator

00:55

Problem 4

Write an equation of the line in slope-intercept form.
The slope is $-7 ;$ the $y$ -intercept is $-\frac{2}{3}$

Nick Johnson

Numerade Educator

00:57

Problem 5

Write an equation of the line in slope-intercept form.
The slope is $-1 ;$ the $y$ -intercept is 3

Nick Johnson

Numerade Educator

00:31

Problem 6

Write an equation of the line in slope-intercept form.
The slope is $-2 ;$ the $y$ -intercept is $0 .$

Nick Johnson

Numerade Educator

00:42

Problem 7

Write an equation of the line in slope-intercept form.
The slope is $-3 ;$ the $y$ -intercept is $\frac{1}{2}$

Nick Johnson

Numerade Educator

00:43

Problem 8

Write an equation of the line in slope-intercept form.
The slope is $4 ;$ the $y$ -intercept is $-6$

Nick Johnson

Numerade Educator

01:13

Problem 9

Suppose that bike rentals cost $\$ 4$ plus $\$ 1.50$ per hour.
Write an equation to model the total cost $y$ of renting a bike for $x$ hours.

Nick Johnson

Numerade Educator

01:00

Problem 10

Suppose that bike rentals cost $\$ 4$ plus $\$ 1.50$ per hour.
Graph the equation. Label the $y$ -intercept

Nick Johnson

Numerade Educator

01:05

Problem 11

Suppose that bike rentals cost $\$ 4$ plus $\$ 1.50$ per hour.
Use the equation to find the cost of renting a bike for 12 hours.

Nick Johnson

Numerade Educator

01:07

Problem 12

Write an equation of the line in slope-intercept form.
The slope is $3 ;$ the $y$ -intercept is $-2$

Nick Johnson

Numerade Educator

00:42

Problem 13

Write an equation of the line in slope-intercept form.
The slope is $1 ;$ the $y$ -intercept is 2

Christopher Stanley

Numerade Educator

01:42

Problem 14

Write an equation of the line in slope-intercept form.
The slope is $0 ;$ the $y$ -intercept is 4

Nick Johnson

Numerade Educator

00:43

Problem 15

Write an equation of the line in slope-intercept form.
The slope is $2 ;$ the $y$ -intercept is $-1$

Nick Johnson

Numerade Educator

00:41

Problem 16

Write an equation of the line in slope-intercept form.
The slope is $\frac{3}{2} ;$ the $y$ -intercept is 3

Nick Johnson

Numerade Educator

01:00

Problem 17

Write an equation of the line in slope-intercept form.
The slope is $-\frac{1}{4} ;$ the $y$ -intercept is 1

Nick Johnson

Numerade Educator

00:46

Problem 18

Write an equation of the line in slope-intercept form.
The slope is $-6 ;$ the $y$ -intercept is $\frac{3}{4}$

Nick Johnson

Numerade Educator

00:56

Problem 19

Write an equation of the line in slope-intercept form.
The slope is $-3 ;$ the $y$ -intercept is $-\frac{1}{2}$

Nick Johnson

Numerade Educator

03:10

Problem 20

Write an equation of the line shown in the graph.
(Graph cannot copy)

Derek Follett

Numerade Educator

03:10

Problem 21

Write an equation of the line shown in the graph.
(Graph cannot copy)

Derek Follett

Numerade Educator

03:10

Problem 22

Write an equation of the line shown in the graph.
(Graph cannot copy)

Derek Follett

Numerade Educator

03:02

Problem 23

Write an equation of each line in slope-intercept form.
(Graph cannot copy)

Nicholas Bondra

Numerade Educator

03:02

Problem 24

Write an equation of each line in slope-intercept form.
(Graph cannot copy)

Nicholas Bondra

Numerade Educator

03:02

Problem 25

Write an equation of each line in slope-intercept form.
(Graph cannot copy)

Nicholas Bondra

Numerade Educator

01:00

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 .

Nick Johnson

Numerade Educator

01:14

Problem 27

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.
Estimate the population of South Carolina in 1996 .

Nick Johnson

Numerade Educator

00:48

Problem 28

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.

Nick Johnson

Numerade Educator

02:20

Problem 29

A rental company charges a flat fee of $\$ 30$ and an additional $\$ .25$ per mile to rent a moving van.
Copy and complete the table using the equation you found in Exercise 28 .
(TABLE CANNOT COPY)

Lisa Tarman

Numerade Educator

00:46

Problem 30

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.

Nick Johnson

Numerade Educator

00:45

Problem 31

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.

Nick Johnson

Numerade Educator

00:43

Problem 32

Write a linear equation to model the situation. Use unit analysis to check your model.
You have walked 5 miles on a hiking trail. You continue to walk at the rate of
2 miles per hour for 6 hours.

Nick Johnson

Numerade Educator

01:32

Problem 33

You are traveling home in a bus whose speed is 50 miles per hour. At noon you are 200 miles from home. Write an equation that models your distance $y$ from home in terms of $t,$ the number of hours since noon. Why does the line given by this equation have a negative slope?

Lisa Tarman

Numerade Educator

00:42

Problem 34

You are designing a calendar as a fund-raising project for your Biology Club. The cost of printing is $\$ 500$, plus S2.50 per calendar.
(Graph cannot copy)
Write an equation to model the total cost $C$ of printing $x$ calendars.

Nick Johnson

Numerade Educator

00:48

Problem 35

You are designing a calendar as a fund-raising project for your Biology Club. The cost of printing is $\$ 500$, plus S2.50 per calendar.
(Graph cannot copy)
You sell each calendar for $\$ 5.00 .$ Write an equation to model the total income $T$ for selling $x$ calendars.

Lisa Tarman

Numerade Educator

04:02

Problem 36

You are designing a calendar as a fund-raising project for your Biology Club. The cost of printing is $\$ 500$, plus S2.50 per calendar.
(Graph cannot copy)
Graph both equations in the same coordinate plane. Estimate the point at which the two lines intersect. Explain the significance of this point of intersection in the context of the real-life problem.

Lisa Tarman

Numerade Educator

01:46

Problem 37

You estimate the club can sell 200 calendars. Write an analysis of how effective this fundraising project will be for the club.

Lisa Tarman

Numerade Educator

00:47

Problem 38

Use the following information. The U.S. Bureau of the Census predicted that the population of Florida would be about 17.4 million in 2010 and then would increase by about 0.22 million per year until 2025
Choose the linear model that predicts the population $P$ of Florida (in millions) in terms of $t,$ the number of years since 2010 .
A) $P=17.4 t+0.22$
(B) $P=-0.22 t+17.4$
(c) $P=0.22 t+17.4$
(D) $P=-17.4 t+0.22$

Nick Johnson

Numerade Educator

00:53

Problem 39

According to the correct model, the population of Florida in 2011 will be about $\underline{?}$ million.
(A) 17.18
(B) 3.8
(C) 17.62
(D) 39.4

Nick Johnson

Numerade Educator

02:59

Problem 40

In January, your ceramics class begins with 12 students. In every month after January, three new students join and one student drops out.
a. Write a linear equation to model the situation.
b. Graph the model.
c. Predict the size of your ceramics class in May and June.

Lisa Tarman

Numerade Educator

00:51

Problem 41

Evaluate the expression when $x=-3$ and $y=6 .$
$$\frac{3 x}{x+y}$$

Nick Johnson

Numerade Educator

00:39

Problem 42

Nick Johnson

Numerade Educator

01:24

Problem 43

Nick Johnson

Numerade Educator

00:51

Problem 44

You are designing a newspaper page with three photos. The page is $13 \frac{1}{4}$ inches wide with 1 inch margins on both sides. You need to allow $\frac{3}{4}$ inch between photographs. How wide should you make the photos if they are of equal size?
Sketch a diagram of the newspaper page.

Lisa Tarman

Numerade Educator

01:54