Algebra 1: Concepts and Skills

Ron Larson, Laurie Boswell, Holt McDougal

Chapter 4

Graphing Linear Equations and Functions - all with Video Answers

Educators

PL

KS

Section 1

The Coordinate Plane

Problem 1

In Exercises $1-3,$ complete the sentence.
Each point in a coordinate plane corresponds to an _____ of real numbers.

PL

Paying Lee

Numerade Educator

Problem 2

In Exercises $1-3,$ complete the sentence.
In the ordered pair (2, 5), the y-coordinate is _____.

Lily An

Numerade Educator

Problem 3

In Exercises $1-3,$ complete the sentence.
The x-axis and the y-axis divide the coordinate plane into four ____.

Lily An

Numerade Educator

Problem 4

Plot and label the ordered pairs in a coordinate plane.
$$
A(4,-1), B(5,0)
$$

Lily An

Numerade Educator

Problem 5

Plot and label the ordered pairs in a coordinate plane.
$$
A(-2,-3), B(-3,-2)
$$

Lily An

Numerade Educator

Problem 6

Complete the statement with always, sometimes, or never.
A point plotted in Quadrant IV ${?}$ has a positive $y$ -value.

Lily An

Numerade Educator

Problem 7

Complete the statement with always, sometimes, or never.
A point plotted in Quadrant IV ${?}$ has a positive $x$ -value.

Lily An

Numerade Educator

Problem 8

Complete the statement with always, sometimes, or never.
A point plotted on the $x$ -axis ${?}$ has $y$ -coordinate $0 .$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 9

Complete the statement with always, sometimes, or never.
A point plotted on the $x$ -axis ? has $y$ -coordinate $0 .$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 10

IDENTIFYING ORDERED PAIRS Write the ordered pairs that correspond to the points labeled $A, B, C,$ and $D$ in the coordinate plane.

Odessa Hilton

Numerade Educator

Problem 11

IDENTIFYING ORDERED PAIRS Write the ordered pairs that correspond to the points labeled $A, B, C,$ and $D$ in the coordinate plane.

Odessa Hilton

Numerade Educator

Problem 12

IDENTIFYING ORDERED PAIRS Write the ordered pairs that correspond to the points labeled $A, B, C,$ and $D$ in the coordinate plane.

Odessa Hilton

Numerade Educator

Problem 13

Plot and label the ordered pairs in a coordinate plane.
$$
A(0,3), B(-2,-1), C(2,0)
$$

Lily An

Numerade Educator

Problem 14

Plot and label the ordered pairs in a coordinate plane.
$$
A(5,2), B(4,3), C(-2,-4)
$$

Lily An

Numerade Educator

Problem 15

Plot and label the ordered pairs in a coordinate plane.
$$
A(4,1), B(0,-3), C(3,3)
$$

Lily An

Numerade Educator

Problem 16

Plot and label the ordered pairs in a coordinate plane.
$$
A(0,0), B(2,-2), C(-2,0)
$$

Lily An

Numerade Educator

Problem 17

Plot and label the ordered pairs in a coordinate plane.
$$
A(-4,1), B(-1,5), C(0,-4)
$$

Lily An

Numerade Educator

Problem 18

Plot and label the ordered pairs in a coordinate plane.
$$
A(3,-5), B(5,3), C(-3,-1)
$$

Lily An

Numerade Educator

Problem 19

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(5,-3)
$$

Lily An

Numerade Educator

Problem 20

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(-2,7)
$$

Lily An

Numerade Educator

Problem 21

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(6,17)
$$

Lily An

Numerade Educator

Problem 22

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(14,-5)
$$

Lily An

Numerade Educator

Problem 23

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(-4,-2)
$$

Lily An

Numerade Educator

Problem 24

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(3,9)
$$

Lily An

Numerade Educator

Problem 25

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(-5,-2)
$$

Lily An

Numerade Educator

Problem 26

Without plotting the point, tell whether it is in Quadrant I, Quadrant II, Quadrant III, or Quadrant IV.
$$
(-5,6)
$$

Lily An

Numerade Educator

Problem 27

CAR COMPARISONS In Exercises $27-32,$ use the scatter plots below to compare the weight of a car to its length and to its gas mileage.
In the Weight vs. Length graph, what are the units on the horizontal axis? What are the units on the vertical axis?

Robin Corrigan

Numerade Educator

Problem 28

CAR COMPARISONS In Exercises $27-32,$ use the scatter plots below to compare the weight of a car to its length and to its gas mileage.
In the Weight vs. Length graph, estimate the coordinates of the point for a car that weighs
about 4000 pounds.

Robin Corrigan

Numerade Educator

Problem 29

CAR COMPARISONS In Exercises $27-32,$ use the scatter plots below to compare the weight of a car to its length and to its gas mileage.
Which of the following is true?
A. Length tends to decrease as weight increases.
B. Length is constant as weight increases.
C. Length tends to increase as weight increases.
D. Length is not related to weight.

Gus Steppen

Numerade Educator

Problem 30

CAR COMPARISONS In Exercises $27-32,$ use the scatter plots below to compare the weight of a car to its length and to its gas mileage.
In the Weight vs. Gas Mileage graph, in the ordered pair (2010, 29), what is the value of W?
What is the value of G?

Robin Corrigan

Numerade Educator

Problem 31

CAR COMPARISONS In Exercises $27-32,$ use the scatter plots below to compare the weight of a car to its length and to its gas mileage.
INTERPRETING DATA In the Weight vs. Gas Mileage graph, how does a car’s gas mileage tend to change as the weight of the car increases?

Gus Steppen

Numerade Educator

Problem 32

CAR COMPARISONS In Exercises $27-32,$ use the scatter plots below to compare the weight of a car to its length and to its gas mileage.
CRITICAL THINKING How would you expect the length of a car to affect its gas mileage? Explain your reasoning.

Robin Corrigan

Numerade Educator

Problem 33

The table shows the wing length (in millimeters) and the wing-beat rate (in beats per second) for five birds.
$$
\begin{array}{|l|c|c|c|c|c|}
\hline \text { Bird } & {\text { Flamingo }} & {\text { Shellduck }} & {\text { Velvet Scoter }} & {\text { Fulmar }} & {\text { Great Egret }} \\
\hline \text { Wing length } & {400} & {375} & {281} & {321} & {437} \\
\hline \text { Wing-beat rate } & {24} & {3.0} & {43} & {3.6} & {21} \\
\hline
\end{array}
$$
Make a scatter plot that shows the wing-beat rates and wing lengths for the five birds. Use the horizontal axis to represent the wing-beat rate.

Gus Steppen

Numerade Educator

Problem 34

The table shows the wing length (in millimeters) and the wing-beat rate (in beats per second) for five birds.
$$
\begin{array}{|l|c|c|c|c|c|}
\hline \text { Bird } & {\text { Flamingo }} & {\text { Shellduck }} & {\text { Velvet Scoter }} & {\text { Fulmar }} & {\text { Great Egret }} \\
\hline \text { Wing length } & {400} & {375} & {281} & {321} & {437} \\
\hline \text { Wing-beat rate } & {24} & {3.0} & {43} & {3.6} & {21} \\
\hline
\end{array}
$$
What is the slowest wing-beat rate shown on the scatter plot? What is the fastest? Where are these located on your scatter plot?

Gus Steppen

Numerade Educator

Problem 35

The table shows the wing length (in millimeters) and the wing-beat rate (in beats per second) for five birds.
$$
\begin{array}{|l|c|c|c|c|c|}
\hline \text { Bird } & {\text { Flamingo }} & {\text { Shellduck }} & {\text { Velvet Scoter }} & {\text { Fulmar }} & {\text { Great Egret }} \\
\hline \text { Wing length } & {400} & {375} & {281} & {321} & {437} \\
\hline \text { Wing-beat rate } & {24} & {3.0} & {43} & {3.6} & {21} \\
\hline
\end{array}
$$
INTERPRETING DATA Describe the relationship between the wing length and the wing-beat rate for the five birds.

Gus Steppen

Numerade Educator

Problem 36

Which ordered pair has an $x$ -coordinate of $-7 ?
(A) $(3,-7)$
(B) $(-7,3)$
(C) $(7,3)$
(D) $(3,7)$

Tiffany Tran

Numerade Educator

Problem 37

The point $(-9,-8)$ is in which quadrant?
(A) Quadrant I
(B) Quadrant II
(C) Quadrant III
(D) Quadrant IV

Lily An

Numerade Educator

Problem 38

Which ordered pair is in Quadrant IV?
(A) $(7,12)$
(B) $(-4,3)$
(C) $(-4,3)$
(D) $(8,-7)$

Lily An

Numerade Educator

Problem 39

The vertical axis is also called the ____ ?
(A) $x-\mathrm{axis}$
(B) $y$ -axis
(C) coordinate plane
(D) origin
The vertical axis is also called the ____ ?
(A) $x-\mathrm{axis}$
(B) $y$ -axis
(C) coordinate plane
(D) origin

Lily An

Numerade Educator

Problem 40

EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable.
$3 x+9$ when $x=2$

Lily An

Numerade Educator

Problem 41

EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable.
$13-(y+2)$ when $y=4$

Lily An

Numerade Educator

Problem 42

EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable.
$4.2 t+17.9$ when $t=3$

Lily An

Numerade Educator

Problem 43

EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable.
$-x-y$ when $x=-2$ and $y=-1$

Lily An

Numerade Educator

Problem 44

USING EXPONENTS Evaluate the expression.
$x^{2}-3$ when $x=4$

Lily An

Numerade Educator

Problem 45

USING EXPONENTS Evaluate the expression.
$$
12+y^{3} \text { when } y=3
$$

Lily An

Numerade Educator

Problem 46

USING EXPONENTS Evaluate the expression.
$$
x^{5}+10 \text { when } x=1.5
$$

Lily An

Numerade Educator

Problem 47

USING EXPONENTS Evaluate the expression.
$$
\frac{a^{2}+b^{2}}{a-b} \text { when } a=2 \text { and } b=3
$$

Lily An

Numerade Educator

Problem 48

ABSOLUTE VALUE Evaluate the expression.
$$
|-2.6|
$$

Lily An

Numerade Educator

Problem 49

ABSOLUTE VALUE Evaluate the expression.
$$
|1.07|
$$

Lily An

Numerade Educator

Problem 50

ABSOLUTE VALUE Evaluate the expression.
$$
\left|\frac{9}{10}\right|
$$

Lily An

Numerade Educator

Problem 51

ABSOLUTE VALUE Evaluate the expression.
$$
\left|\frac{-2}{3}\right|
$$

Lily An

Numerade Educator

Problem 52

SOLVING EQUATIONS Solve the equation.
$$
3 x-6=0
$$

Lily An

Numerade Educator

Problem 53

SOLVING EQUATIONS Solve the equation.
$$
6 x+5=35
$$

Lily An

Numerade Educator

Problem 54

SOLVING EQUATIONS Solve the equation.
$$
x+1=-3
$$

Lily An

Numerade Educator

Problem 55

SOLVING EQUATIONS Solve the equation.
$$
a-3=-2
$$

Lily An

Numerade Educator

Problem 56

SOLVING EQUATIONS Solve the equation.
$$
\frac{1}{2} x-1=-1
$$

Lily An

Numerade Educator

Problem 57

SOLVING EQUATIONS Solve the equation.
$$
\frac{1}{5} r+3=4
$$

Lily An

Numerade Educator

Problem 58

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
7 \frac{4}{9}-4 \frac{1}{9}
$$

Lily An

Numerade Educator

Problem 59

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
3 \frac{2}{3}-1 \frac{1}{3}
$$

Lily An

Numerade Educator

Problem 60

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
8 \frac{3}{4}-7 \frac{3}{4}
$$

Lily An

Numerade Educator

Problem 61

Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$9 \frac{8}{15}-2 \frac{4}{15}$

Heather Zimmers

Heather Zimmers

Numerade Educator

Problem 62

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
8 \frac{9}{13}-5 \frac{2}{13}
$$

Lily An

Numerade Educator

Problem 63

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
6 \frac{7}{11}-6 \frac{2}{11}
$$

Lily An

Numerade Educator

Problem 64

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
17 \frac{5}{8}-10 \frac{3}{8}
$$

Lily An

Numerade Educator

Problem 65

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
12 \frac{17}{21}-7 \frac{2}{21}
$$

Lily An

Numerade Educator

Problem 66

SUBTRACTING FRACTIONS Subtract. Write the answer as a fraction or as a mixed number in simplest form.
$$
18 \frac{9}{14}-3 \frac{3}{14}
$$

Lily An

Numerade Educator