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Algebra 1 Common Core

Randall I. Charles,Basia Hall, Dan Kennedy

Chapter 5

Linear Functions - all with Video Answers

Educators

Section 1

Rate of Change and Slope

02:06

Problem 1

Is the rate of change in cost constant with respect to the number of pencils bought? Explain.

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01:20

Problem 2

What is the slope of the line.

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Heather Zimmers
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00:46

Problem 3

What is the slope of the line through $(-1,2)$ and $(2,-3) ?$

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Heather Zimmers
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00:39

Problem 4

Vocabulary What characteristic of a graph represents the rate of change? Explain.

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02:08

Problem 5

Open-Ended Give an example of a real-world situation that you can model with a horizontal line. What is the rate of change for the situation? Explain.

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01:40

Problem 6

Compare and Contrast How does finding a line's slope by counting units of vertical and horizontal change on a graph compare with finding it using the slope formula?

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Heather Zimmers
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00:46

Problem 7

Error Analysis A student calculated the slope of the line at the right to be 2. Explain the mistake. What is the correct slope?

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Heather Zimmers
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01:13

Problem 8

Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.

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Heather Zimmers
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01:40

Problem 9

Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.

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Heather Zimmers
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01:59

Problem 10

Determine whether each rate of change is constant. If it is, find the rate of change and explain what it represents.

Khushbu Rani
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01:15

Problem 11

Find the slope of each line.

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01:07

Problem 12

Find the slope of each line.

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01:11

Problem 13

Find the slope of each line.

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Heather Zimmers
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01:15

Problem 14

Find the slope of each line.

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Heather Zimmers
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01:23

Problem 15

Find the slope of each line.

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Heather Zimmers
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01:25

Problem 16

Find the slope of each line.

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Heather Zimmers
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00:40

Problem 17

Find the slope of the line that passes through each pair of points.
$$
(0,0),(3,3)
$$

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00:41

Problem 18

Find the slope of the line that passes through each pair of points.
$$
(1,3),(5,5)
$$

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00:38

Problem 19

Find the slope of the line that passes through each pair of points.
$$
(4,4),(5,3)
$$

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Heather Zimmers
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00:41

Problem 20

Find the slope of the line that passes through each pair of points.
$$
(0,-1),(2,3)
$$

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00:42

Problem 21

Find the slope of the line that passes through each pair of points.
$$
(-6,1),(4,8)
$$

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00:46

Problem 22

Find the slope of the line that passes through each pair of points.
$$
(2,-3),(5,-4)
$$

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Heather Zimmers
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00:35

Problem 23

Find the slope of each line.

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00:41

Problem 24

Find the slope of each line.

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00:34

Problem 25

Find the slope of each line.

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00:42

Problem 26

Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.

The length of a bus route is 4 milong on the sixth day and 4 milong on the
seventeenth day.

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00:58

Problem 27

Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.

A babysitter earns $\$ 9$ for 1 h and $\$ 36$ for 4 .

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01:00

Problem 28

Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.

A student earns a 98 on a test for answering one question incorrectly and earns a 90
for answering five questions incorrectly.

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Heather Zimmers
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00:58

Problem 29

Without graphing, tell whether the slope of a line that models each linear relationship is positive, negative, zero, or undefined. Then find the slope.

The total cost, including shipping, for ordering five uniforms is $\$ 66 .$ The total cost,
including shipping, for ordering nine uniforms is $\$ 114$.

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Heather Zimmers
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01:13

Problem 30

State the independent variable and the dependent variable in each linear relationship. Then find the rate of change for each situation.

Snow is $0.02 \mathrm{m}$ deep after $1 \mathrm{h}$ and $0.06 \mathrm{m}$ deep after $3 \mathrm{h}$

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01:05

Problem 31

State the independent variable and the dependent variable in each linear relationship. Then find the rate of change for each situation.

The cost of tickets is $\$ 36$ for three people and $\$ 84$ for seven people.

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01:06

Problem 32

State the independent variable and the dependent variable in each linear relationship. Then find the rate of change for each situation.

A car is $200 \mathrm{km}$ from its destination after $1 \mathrm{h}$ and $80 \mathrm{km}$ from its destination after $3 \mathrm{h}$

Heather Zimmers
Heather Zimmers
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00:46

Problem 33

Use the slope formula to find the slope of the line that passes through each pair of points. Then plot the points and sketch the line that passes through them Does the slope you found using the formula match the direction of the line you sketched?
$$
(-2,1),(7,1)
$$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:56

Problem 34

Use the slope formula to find the slope of the line that passes through each pair of points. Then plot the points and sketch the line that passes through them Does the slope you found using the formula match the direction of the line you sketched?
$$
(4.25,0),(3.5,3)
$$

Heather Zimmers
Heather Zimmers
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00:52

Problem 35

Use the slope formula to find the slope of the line that passes through each pair of points. Then plot the points and sketch the line that passes through them Does the slope you found using the formula match the direction of the line you sketched?
$$
\left(-\frac{1}{2}, \frac{4}{7}\right),\left(8, \frac{4}{7}\right)
$$

Heather Zimmers
Heather Zimmers
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01:06

Problem 36

Use the slope formula to find the slope of the line that passes through each pair of points. Then plot the points and sketch the line that passes through them Does the slope you found using the formula match the direction of the line you sketched?
$$
(-5,0.124),(-5,-0.584)
$$

Heather Zimmers
Heather Zimmers
Numerade Educator
01:00

Problem 37

Use the slope formula to find the slope of the line that passes through each pair of points. Then plot the points and sketch the line that passes through them Does the slope you found using the formula match the direction of the line you sketched?
$$
(-42.25,5.2),(3.25,3)
$$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:59

Problem 38

Use the slope formula to find the slope of the line that passes through each pair of points. Then plot the points and sketch the line that passes through them Does the slope you found using the formula match the direction of the line you sketched?
$$
\left(-2, \frac{2}{11}\right),\left(-2, \frac{7}{13}\right)
$$

Heather Zimmers
Heather Zimmers
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01:18

Problem 39

Think About a Plan The graph shows the average growth rates for three different animals. Which animal's growth shows the fastest rate of change? The slowest rate of change?
$\cdot$ How can you use the graph to find the rates of change?
$\cdot$ Are your answers reasonable?

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00:53

Problem 40

Find two points that lie on a line with slope $-9 .$

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01:03

Problem 41

Profit John's business made $\$ 4500$ in January and $\$ 8600$ in March. What is the rate of change in his profit for this time period?

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Heather Zimmers
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01:17

Problem 42

Each pair of points lies on a line with the given slope. Find $x$ or $y .$
$$
(2,4),(x, 8) ; \text { slope }=-2
$$

Heather Zimmers
Heather Zimmers
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00:50

Problem 43

Each pair of points lies on a line with the given slope. Find $x$ or $y .$
$$
(4,3),(5, y) ; \text { slope }=3
$$

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Heather Zimmers
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01:04

Problem 44

Each pair of points lies on a line with the given slope. Find $x$ or $y .$
$$
(2,4),(x, 8) ; \text { slope }=-\frac{1}{2}
$$

Heather Zimmers
Heather Zimmers
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01:03

Problem 45

Each pair of points lies on a line with the given slope. Find $x$ or $y .$
$$
(3, y),(1,9) ; \text { slope }=-\frac{5}{2}
$$

Heather Zimmers
Heather Zimmers
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00:50

Problem 46

Each pair of points lies on a line with the given slope. Find $x$ or $y .$
$$
(-4, y),(2,4 y) ; \text { slope }=6
$$

Heather Zimmers
Heather Zimmers
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00:45

Problem 47

Each pair of points lies on a line with the given slope. Find $x$ or $y .$
$$
(3,5),(x, 2) ; \text { undefined slope }
$$

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Heather Zimmers
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00:51

Problem 48

Is it true that a line with slope 1 always passes through the origin? Explain your reasoning.

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Heather Zimmers
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02:33

Problem 49

Arithmetic sequences Use the arithmetic sequence $10,15,20,25, \ldots$
a. Find the common difference of the sequence.
b. Let $x=$ the term number, and let $y=$ the corresponding term of the sequence. Graph the ordered pairs $(x, y)$ for the first eight terms of the sequence. Draw a line through the points.
c. Reasoning How is the slope of a line from part (b) related to the common difference of the sequence?

Heather Zimmers
Heather Zimmers
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01:03

Problem 50

Do the points in each set lie on the same line? Explain your answer.
$$
A(1,3), B(4,2), C(-2,4)
$$

Heather Zimmers
Heather Zimmers
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00:53

Problem 51

Do the points in each set lie on the same line? Explain your answer.
$$
G(3,5), H(-1,3), I(7,7)
$$

Heather Zimmers
Heather Zimmers
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00:52

Problem 52

Do the points in each set lie on the same line? Explain your answer.
$$
D(-2,3), E(0,-1), F(2,1)
$$

Heather Zimmers
Heather Zimmers
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01:02

Problem 53

Do the points in each set lie on the same line? Explain your answer.
$$
P(4,2), Q(-3,2), R(2,5)
$$

Heather Zimmers
Heather Zimmers
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01:00

Problem 54

Do the points in each set lie on the same line? Explain your answer.
$$
G(1,-2), H(-1,-5), I(5,4)
$$

Heather Zimmers
Heather Zimmers
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00:57

Problem 55

Do the points in each set lie on the same line? Explain your answer.
$$
S(-3,4), T(0,2), X(-3,0)
$$

Heather Zimmers
Heather Zimmers
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01:12

Problem 56

Find the slope of the line that passes through each pair of points.
$$
(a,-b),(-a,-b)
$$

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Heather Zimmers
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00:51

Problem 57

Find the slope of the line that passes through each pair of points.
$$
(-m, n),(3 m,-n)
$$

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Heather Zimmers
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00:35

Problem 58

Find the slope of the line that passes through each pair of points.
$$
(2 a, b),(c, 2 d)
$$

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Heather Zimmers
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