6-2
6-2
Slope-Intercept Form
1. Plan
GO for Help
What You’ll Learn
Check Skills You’ll Need
• To write linear equations in
Evaluate each expression.
slope-intercept form
• To graph linear equations
. . . And Why
To use a graph to relate total
earnings to sales, as in
Example 5
Lessons 1-2 and 2-3
The word linear contains
the word “line”.
To write linear equations in
slope-intercept form
To graph linear equations
2. -2x - 5 for x = 3 –11
2
3. 14 x + 2 for x = 16 6
4. 0.2x + 2 for x = 15 5
Examples
5. 8 - 5n for n = 3 –7
1
6. -4p + 9 for p = 2 1
New Vocabulary • linear equation • parent function • linear parent function
• y-intercept • slope-intercept form
y
yx2
y
2
y
4
y x
2
yx
2 x
O
2
0
2(0) 1
1
1
2(1) 1
1
2
2(2) 1
3
Lesson Planning and
Resources
y
See p. 306E for a list of the
resources that support this lesson.
y
PowerPoint
1
O
Bell Ringer Practice
2
x
4
Exponents and Order of
Operations
1 2 (23)
If you know the slope of a line and its y-intercept, you can write the equation of
the line. The letter m refers to the slope.
Lesson 6-2 Slope-Intercept Form
Below Level
L1
learning style: tactile
Check Skills You’ll Need
For intervention, direct students to:
3
Two points on the line are (0, 1) and (2, -3). The slope is 0 2 2 5 242 or -2.
The y-intercept is the y-coordinate of the point where a line crosses the y-axis.
Since y = -2x + 1 crosses the y-axis at (0, 1), the y-intercept is 1.
Have students graph the equation y = 2x - 1 for
several values of x, and then measure the slope in
terms of rise over run. Have them discover that the
coefficient of x in this form of an equation is the slope
of the line.
In upper level mathematics, lines
are considered curves. If the slope
of a curve is constant, it is a line.
Constant slope is the defining
characteristic of a line.
3 y 1–x 1
3
The equation of a line gives important information about
its graph. Consider the table and graph of the equation
y = -2x +1.
2x 1
Math Background
x
4
The functions shown above all graph as lines. A parent function is the
simplest equation of a function. The equation y = x or ƒ(x) = x is the
linear parent function for all equations that graph as lines.
x
Identifying Slope and
y-Intercept
Writing an Equation
Writing an Equation From
a Graph
Graphing Equations
Real-World Problem Solving
More Math Background: p. 306C
2
x
yx
1
2
yx
O
2
3
4
5
An equation whose graph is a line is a linear equation. A variable in a linear
equation cannot be raised to a power other than 1. So y = 2x is a linear equation
but y = x 2 or y = 2 x are not. All linear equations are related.
3
Special Needs
1
1. 6a + 3 for a = 2 15
61Part 1Writing
Linear
Equations
Writing
Linear
Equations
Vocabulary Tip
Objectives
Lesson 1-2: Example 2
Extra Skills and Word
Problem Practice, Ch. 1
Multiplying and Dividing
Rational Numbers
Lesson 2-3: Example 2
Extra Skills and Word
Problem Practice, Ch. 2
317
L2
In Example 5, help students relate the slope and
y-intercept to what they represent in the
problem.
learning style: verbal
317
2. Teach
Key Concepts
Guided Instruction
2
Error Prevention
EXAMPLE
The point where a line crosses
the y-axis is always of the form
(0, y). Some students may want
to write the y-intercept as these
coordinates. Explain to students
that only the y-coordinate of the
above point is defined as the
y-intercept.
4
5
A
A
B
B
E
D
E
D
C
B
E
D
C
B
A
3
C
B
A
2
C
C
D
D
Slope-Intercept Form of a Linear Equation
The slope-intercept form of a linear equation is y = mx + b.
c
c
slope y-intercept
E
D
C
B
A
1
Definition
E
E
Test-Taking Tip
As you do homework,
make a list of
formulas you can use
later to study for
quizzes and tests.
1
Identifying Slope and y-Intercept
EXAMPLE
What are the slope and y-intercept of y = 3x - 5?
y = mx + b
Use the slope-intercept form.
y = 3x + (-5)
Think of y ≠ 3x – 5 as y ≠ 3x ± (–5).
The slope is 3; the y-intercept is -5.
PowerPoint
Quick Check
Additional Examples
1 What are the slope and
y-intercept of y = 2x - 3?
Slope is 2; y-intercept is –3
1 a. Find the slope and y-intercept of y = 7 x - 3. m ≠ 7 ; b ≠ –3
4
6
4
6
b. Critical Thinking For the equation in Example 1, what happens to the graph of
the line and to the equation if the y-intercept is moved down 3 units?
The line shifts 3 units down; the equation becomes y ≠ 3x – 8.
2
Write an equation of the line with slope 38 and y-intercept 6.
2 Write an equation of the line
with slope 25 and y-intercept 4.
y ≠ 25 x ± 4
3 Write the equation for
the line. y ≠ – 23 x ± 1
4
2
Quick Check
y
2
O
2
y = mx + b
Use the slope-intercept form.
y = 38 x + 6
Substitute 3
8 for m and 6 for b.
2 Write an equation of a line with slope m 5 2 and y-intercept b 5 21. y ≠ 2x – 1
5
5
3
(0, 1)
EXAMPLE
Writing an Equation From a Graph
Multiple Choice Which equation models the linear
function shown in the graph?
x
4
Writing an Equation
EXAMPLE
2
4
(3, 1)
y 5 2 34 x 1 2
y 5 2x 2 43x
4
y 5 2 43x 1 2
y 5 2x 2 34
Find the slope. Two points on the line are (0, 2)
and (4, -1).
For: Slope-Intercept Activity
Use: Interactive Textbook, 6-2
4
y
1
2
O
2
x
5
2
2 2 = 23
slope = 214 2
4
0
The y-intercept is 2. Write an equation in slope-intercept form.
y = mx + b
y = 234 x + 2
Substitute 234 for m and 2 for b.
The equation is y 5 234x 1 2. So the answer is A.
Quick Check
318
3 a. Write the equation of the line using the points (0, 1)
and (2, 2). y 5 12 x 1 1
b. Critical Thinking Does the equation of the line
change if you use (-2, 0) instead of (2, 2)? Explain.
No; any two points will give the same slope.
2 O
y
x
2
4
Chapter 6 Linear Equations and Their Graphs
Advanced Learners
English Language Learners ELL
L4
Challenge students to arrange the following linear
equations in order from steepest to least steep.
y = 12 x + 3, y = 23 x + 3, y = 2x + 3
318
2
learning style: verbal
Students may wonder why m is used to represent
slope in English. There is really no reason other than
custom, but students may find it helpful to relate m to
mountain slope.
learning style: verbal
4
Graphing Linear Equations
Each point on the graph of an equation is an ordered pair that makes the
equation true. The graph of a linear equation is a line that indicates all the
solutions of the equation. You can use the slope and y-intercept to graph a line.
4
Step 1
The y-intercept is –1.
So plot a point at
(0, –1).
y
y
1 O
2
Additional Examples
Step 2
3
The slope is 3, or 1 .
Use the slope to plot
a second point.
y
2
2
2x
᎐2
O
2
᎐2
x
2
x
2
y
right 1
O
2
x
᎐2
2
x
5 The base pay for a used car
salesperson is $300 per week.
The salesperson also earns
15% commission on sales made.
The equation t = 300 + 0.15s
relates total earnings t to sales s.
Graph the equation.
EXAMPLE
Real-World
Weekly Earnings for a
Used Car Salesman
Problem Solving
Commission The base pay of a water-delivery person is $210 per week. He also
earns 20% commission on any sale he makes. The equation t = 210 + 0.2s relates
total earnings t to sales s. Graph the equation.
Step 1 Identify the slope and y-intercept.
t = 210 + 0.2s
t = 0.2s + 210
Connection
Rewrite the equation in
slope-intercept form.
c
y-intercept
Step 2 Plot two points. First plot (0, 210), the
y-intercept. Then use the slope to plot
a second point.
20
2
The slope is 0.2, which equals 10
, or 100 .
Plot a second point 20 units above and 100
units to the right of the y-intercept.
Step 3 Draw a line through the points.
Quick Check
Weekly Earnings for a
Water-Delivery Person
Total Earnings
(dollars)
c
slope
Real-World
6
4
O
When you graph equations for real-world situations, use scales on the x- and
y-axes that are reasonable for the situation. Recall that you can avoid having a
large blank space in a graph by using a zigzag line to show a break in a scale.
Between 1990 and 1999, the
sales of bottled water in the
United States increased
107.6%, which means that
sales more than doubled.
2
2
4 Graph y = 3 x - 2. See left.
2
5
O
⫺2
⫺2
Quick Check
4 Graph y = 13 x - 2.
y
Step 3
Draw a line through
the two points.
up 3
2
Connection to
Geometry
PowerPoint
Graphing Equations
EXAMPLE
Graph y = 3x - 1.
4.
EXAMPLE
Remind students that a line is
made of an infinite number of
points and extends in opposite
directions forever.
260 t
220
0
s
100 200 300
Sales (dollars)
5 Suppose the base pay of the delivery person is $150, and his commission on each
sale is 30%. The equation relating his total earnings t to sales s is t = 150 + 0.3s.
Graph the equation. See back of book.
Lesson 6-2 Slope-Intercept Form
360
y
345
330
315
300
O
x
100 200 300
Sales (dollars)
Resources
• Daily Notetaking Guide 6-2 L3
• Daily Notetaking Guide 6-2—
L1
Adapted Instruction
240
200
Total Earnings (dollars)
2
1
319
Closure
Ask: How does changing the
value of m affect the graph of
a line? Changing m changes
the slope, or slant, of a line.
How does changing the value of
b affect the graph of a line?
Changing b changes the
y-intercept.
319
EXERCISES
3. Practice
For more exercises, see Extra Skill and Word Problem Practice.
Practiceand
andProblem
ProblemSolving
Solving
Practice
Assignment Guide
A
Practice by Example
1 A B 1-27, 41-49, 56-62,
Example 1
65-71
2 A B
28-40, 50-55, 63, 64,
72-74
C Challenge
75-79
(page 318)
GO for
Help
Example 2
80-83
84-88
Homework Quick Check
To check students’ understanding
of key skills and concepts, go over
Exercises 24, 38, 57, 62, 64.
Example 3
(page 318)
Teaching Tip
Exercises 22–27 Suggest that
22. y ≠ –23 x ± 1
students use both intercepts to
determine the slope whenever
possible.
23. y ≠ 34 x ± 2
4. y = 5x + 8 5; 8
10. m = 92 , b = 3
13. m = 0, b = 1
11. m = 3, b = 29
14. m = -1, b = -6
16. m = 0.3, b = 4
17. m = 0.4, b = 0.6
19. m = 2 15 , b = 2 25
20. m = 2 14 , b = 54
26. y ≠ –25 x ± 14
5
may confuse the slope and
y-intercept when graphing.
Tell them to begin at b, and
then move m (using rise and run).
27. y ≠ 54 x – 12
22.
4
2
3
x
2
O
(page 319)
L2
Practice
Name
L1
Class
L3
Date
Practice 6-2
Slope-Intercept Form
Example 5
Find the slope and y-intercept of each equation. Then graph.
2. y + 3 = 2 13 x
1. y = x + 2
5. y = 12 x - 4
9. y = -x - 2
4. y - 35 x = -1
8. y + 13 x = -2
3. y = 2x - 1
6. y - 2x = -3
7. y = 25 x + 3
10. y - 6 = -2x
11. y = -5x - 2
12. y + x = 0
13. y + 4 = 2x
14. y = -5x + 5
15. y = -4 + x
16. y = -4x
17. y = 45 x + 2
21. y = 2 47 x + 6
18. y - 34 x = -5
19. y = -6
20. y - 3 = 2 23 x
(page 319)
24. y = 37 x
23. y + 15 x = -2
22. y + 3x = 6
Write an equation of a line with the given slope and y-intercept.
25. m = 4, b = 8
26. m = -2, b = -6
28. m = 2 95 , b = -7
29. m = -6, b = 1
27. m = 34 , b = 0
30. m = 73 , b = -1
32. m = 9, b = 4
33. m = -8, b = 11
35. m = -11, b = 13
36. m = 2 72 , b = -6
31. m = 2 15 , b = -3
34. m = 92 , b = 0
B
Write the slope-intercept form of the equation for each line.
38.
3
1
21
40.
211
y
41.
y
3
2
1
1
4
3
2
1
O x
x
O
1 2 3
O
1 y
O
21
2
3
4
39.
y
x
1 2
4
3
2
1
321
42.
1
x
1 2
21
1
2
3
y
Apply Your Skills
1 2 3
y
x
O
1 2
43. A television production company charges a basic fee of $4000 and then
$2000 per hour when filming a commercial.
a. Write an equation in slope-intercept form relating the basic fee
and per-hour charge.
b. Graph your equation.
y
2
1
10. y ≠ 29 x ± 3
11. y ≠ 3x ± 92
12. y ≠ 92 x ± 3
320
Exercises
2
x
4
2
27.
y
2
4
O
2
2
x
O
2x
28. y = 12 x + 4
29. y = 23 x - 1
30. y = -5x + 2
31. y = 2x + 5
32. y = x + 4
33. y = -x + 2
34. y = 4x - 3
35. y = 2 32 x
36. y = 25 x - 3
37. y = 2 23 x + 2
38. y = 2 45x + 4
39. y = -0.5x + 2
40. Retail Sales A music store is offering a coupon promotion on its CDs. The
regular price for CDs is $14. With the coupon, customers are given $4 off the
total purchase. The equation t = 14c - 4, where c is the number of CDs and
t is the total cost of the purchase, models this situation.
a. Graph the equation. See margin p. 322.
b. Find the total cost for a sale of 6 CDs. $80
Find the slope and y-intercept of each equation.
42. y + 12 x = 0 –12 ; 0
45. 2y - 6 = 3x 32 ; 3
43. y - 9x = 12 9; 12
46. -2y = 6(5 - 3x) 9; –15
48. y = (2 - a)x + a
2 – a; a
49. 2y + 4n = -6x
–3; –2n
Chapter 6 Linear Equations and Their Graphs
16. y ≠ 0.3x ± 4
19. y ≠ –51 x – 25
14. y ≠ –x – 6
17. y ≠ 0.4x ± 0.6
20. y ≠ –41 x ± 54
21. y ≠ 83 x ± 23
±5
y
3
13. y ≠ 1
15. y ≠
x
Use the slope and y-intercept to graph each equation. 28–39. See margin.
47. y - d = cx c; d
–23 x
2
x
3
c. Use your graph to find the production costs if 4 hours of filming
were needed.
pages 320–323
O
2
O
26.
44. y = 3x - 9 3;–9
320
2
y
2
41. y - 2 = -3x –3; 2
x
O
© Pearson Education, Inc. All rights reserved.
37.
4
1
L4
Adapted Practice
2
1
4
2
25.
24.
y
3
Example 4
Reteaching
18. m = -7, b = 13
21. m = 38 , b = 23
2
L3
Enrichment
23.
y
O
GPS Guided Problem Solving
12. m = 92 , b = 3
15. m = 2 23 , b = 5
Write the slope-intercept form of the equation for each line. 22–27. See left.
25. y ≠ 12 x ± 12
Exercises 28–39 Some students
8. y = -0.7x - 9 –0.7;–9 9. y = 2 34 x - 5 –34 ; –5
Write an equation of a line with the given slope and y-intercept. 10–21. See margin.
24. y ≠ 2x – 2
Auditory Learners
3. y = x - 54 1; –54
6. y = -4x –4; 0
2. y = 2 12 x + 2 –12 ; 2
5. y = 23 x + 1 23 ; 1
1. y = -2x + 1 –2; 1
7. y = -x - 7 –1; –7
(page 318)
Test Prep
Mixed Review
Find the slope and y-intercept of each equation.
18. y ≠ –7x ±
1
3
Math Tip
Use the slope and y-intercept to graph each equation. 50–53. See margin.
pp. 322–323.
50. y = 7 - 3x
51. 2y + 4x = 0
52. 3y + 6 = -2x
Exercises 51–55 Remind students
to begin by solving for y.
53. y + 2 = 5x - 4
58. Airplane Fuel The graph shows
Weight vs. Fuel on Board
2600
the relationship between the
number of gallons of fuel in the
2580
tank of an airplane and the
(8, 2560)
2560
weight of the airplane. The
equation y = 6x + 2512,
2540
where x is the number of gallons
2520
of fuel and y is the weight of the
(0, 2512)
airplane, models this situation.
2500
a. What does the slope represent?
b. Use the equation to predict the
0
2
4
6
8 10 12
weight of the plane when the
Fuel (gal)
tank contains 25 gallons of fuel. 2662 lb
a. Slope represents the weight of a gallon of fuel.
Is the ordered pair on the graph of the given equation?
Real-World
Connection
Careers Airport ground crews
direct airplanes to and from
their gates.
32.
5
4
4
2
x
y ≠ –x ± 2
y
x
2
y ≠ 4x – 3
y
O
1
1x
3
35.
2
y ≠ –32 x
y
x
3
O
y≠x±4
O
O
34.
O
2
2
y
x
y
1
14
x
2
2
33.
y
O
y
O
2 1
x
2 O
no
1
y ≠ 2x ± 5
y
2
61. (0, -1); y = x - 54
60. (-6, 5); y = 2 12 x + 2
59. (-3, 4); y = -2x + 1
no
yes
62. Multiple Choice At the right is the
graph of y 5 14x 2 2. Which of the
graphs below represents the linear
function if the slope is doubled and the
y-intercept stays the same? C
31.
2
Weight (lb)
56. The slope was
used for the y-int.,
and the y-int. was
used for the slope.
54. 4x + 3y = 2x - 1
55. -2(3x - 4) + y = 0
54–55. See back of book.
56. Error Analysis Fred drew the graph at the right for the
y
equation y = -2x + 1. What error did he make? See left.
2
57. a. A candle begins burning at time t = 0. Its original
–2 O
2 x
GPS height is 12 in. After 30 min the height of the candle is
–2
8 in. Draw a graph showing the change in the height of
the candle. See back of book.
b. Write an equation that relates the height of the candle
2
to the time it has been burning. h ≠ –15
t ± 12
c. How many minutes after the candle is lit will it burn out? 90 min
x
4
2
36.
y
x
O
2
y ≠ 25 x – 3
4
2
y
37.
y
O
GO
4
1
nline
x
O
1
x
2
x
O
2
Homework Help
y ≠ –23 x ± 2
y
1
38.
Visit: PHSchool.com
Web Code: ate-0602
3
y
2
x
Lesson 6-2 Slope-Intercept Form
lesson quiz, PHSchool.com, Web Code: ata-0602
28.
y ≠ 12 x ± 4
y
x
O
1
O
2
2
29.
2
y ≠ 23 x – 1
y
x
2
30.
1
O
1
321
y ≠ –5x ± 2
y
x
1
O
2
4
y ≠ –45 x ± 4
39.
y
1
O
x
1 2 3
y ≠ –0.5x ± 2
321
4. Assess & Reteach
63. Pet Care When the Bryants leave town for a vacation, they put their dog Tyco
in a kennel. The kennel charges $15 for a first-day flea bath and $5 per day. The
equation t = 15 + 5d relates the total charge t to the number of days d.
a. Rewrite the equation in slope-intercept form. t ≠ 5d ± 15
b. Graph the equation. See margin.
c. Explain why the line you graph should lie only in Quadrant I. See margin.
PowerPoint
Lesson Quiz
Find the slope and y-intercept of
each equation.
64. Writing Explain the steps you would use to graph y = 34 x + 5. See margin.
1. y = 43 x - 3 m ≠ 34 ; b ≠ –3
2. y = -2x m ≠ –2; b ≠ 0
65. Critical Thinking Which graphed line has the greater slope? Explain.
Write an equation of a line with
the given slope and
y-intercept.
3. m = -53 , b = -4
y ≠ – 35 x – 4
4. m = 0.5, b = 1 y ≠ 0.5x ± 1
5. Write an equation for the line.
y ≠ 12 x – 3
4
A.
66
Real-World
In the United States, although
35% of households have pet
cats and 37% have pet dogs,
there are about 25% more
pet cats than pet dogs.
y
x
4
2
4
1
6
(6, 0)
1
(0, 3)
x
O
3
3
y
2
x
2
O
2
4
62
20
2
4
C
Challenge
66. (3, 5), (5, 9) y ≠ 2x – 1 67. (5, –13), (2, –1)
68. (–4, 10), (6, 5)
y ≠ –4x ± 7
y ≠ 21 x ± 8
69. (8, 7), (–12, 2)
70. (–7, 4), (11, –14)
71. (–1, –9), (2, 0) 2
y ≠ 3x – 6
y≠1
y ≠ –x – 3
4x ± 5
72. Graphing Calculator Suppose you want to graph the equation y = 54 x - 3.
Enter each key sequence and display the graph. a–b. See left.
a. Y= 5
3
b. Y=
3
4
5
4
x
3
⫺3
Find the value of a such that the graph of the equation has the given slope.
75. y = 2ax + 4; m = -1–12 76. y = 2 12 ax - 5; m = 52
–5
Alternative Assessment
9
77. y = 43 ax + 3; m = 16
4
3
78. a. Geometry Graph these equations on the same grid. a–c. See margin.
y=3
y = -3
x=2
x = -2
b. What geometric figure did you draw? Justify your answer.
c. Draw a diagonal of the figure. What is the equation of this line? Explain.
79b.
r
150
d
O
10
r ≠ –15d ± 265
322
79. Recreation A group of mountain climbers begin an expedition with 265 lb of
food. They plan to eat a total of 15 lb of food per day.
a. Write an equation in slope-intercept form relating the remaining food supply
r to the number of days d. r ≠ –15d ± 265
b. Graph your equation. See left.
c. The group plans to eat the last of their food the day their expedition ends.
Use your graph to find how many days they expect the expedition to last.
18 days
Chapter 6 Linear Equations and Their Graphs
pages 320–322
Exercises
40a. t ≠ 14c – 4
100
50.
t
y
6
60
2
20
c
O
322
60
x
0
1
2
3
4
5
0
1
2
3
4
5
10 S 8 ≠ 2 ≠ slope in B.
A; slope in A ≠ 4.5
4
Given two points on a line, write the equation of the line in slope-intercept form.
x
74. Open-Ended Write a linear equation.
Identify the slope and y-intercept. Then
graph your equation. Check students’ work.
6
Give each student a laminated
coordinate plane and a piece of
uncooked spaghetti. Instruct
each student to write an equation
for a line whose y-intercept is an
integer, and then model the
equation with the spaghetti.
Repeat.
40
c. Which equation gives you the graph of y = 54 x - 3? Explain.
Both; check students’ work.
73. a. What is the slope of each line? 14; 14
y
3
b. What is the y-intercept of each line? 2; –2
c. Geometry The lines in the graph are parallel.
What appears to be true about the slopes of
⫺3
O
parallel lines? same slopes
6. Graph y = -x + 3.
4
64
Connection
72a–b.
2
y
60
y
O
68
80
2
2
B.
y
2
4
6
O
x
2
y ≠ 7 – 3x
Test Prep
Test Prep
Standardized
Test Prep
Multiple Choice
80. Which equation has the same y-intercept as y = 4x - 3? D
A. y - 3 = x
B. y = 8x + 3
C. 3 - y = 4x
D. y = -3 + 8x
81. Which of the following is the equation of the line that has the same slope
as y = 23
2x + 2 and the same y-intercept as y = 3x - 2? G
F. y - 2 = 23
2x
H. y + 2 = 23
2
G. 23
2x = y + 2
J. 23
2x = y + 3
Exercise 80 Suggest to students
82. A software company started with 2 employees. In 6 months, the company
had 7 employees. The number of employees increased at a steady rate.
Which equation models the relationship between the number of
employees n and the number of months m since the company started? A
Short Response
A. n = 5
6m + 2
5
B. m = 2n + 6
C. n = 6
5m + 2
D. m = 5
6n + 2
Resources
For additional practice with a
variety of test item formats:
• Standardized Test Prep, p. 369
• Test-Taking Strategies, p. 364
• Test-Taking Strategies with
Transparencies
that they first check for equations
that have already been solved
for y.
63b.
t ≠ 5d ± 15
t
20
83. A line passes through the points (0, 3) and (1, 5). Graph this line and find
an equation for the line in slope-intercept form. Show your work. See margin.
d
O
Mixed Review
GO for
Help
Lesson 6-1
Review page 166
c. Answers may vary.
Sample: no neg. charges
and no neg. number of
days
Find the slope of the line that passes through each pair of points.
84. (-2, 8), (5, -1)–79 85.(0, 0), (-6, 5)–56 86. (4, 6), (2, -3) 92
87. (1, 2), (2, 1)–1
88. The greeting card industry sells over 6 billion cards annually. Women purchase
80% of all greeting cards sold. How many cards do women purchase annually?
4.8 billion
A P int in Time
1500
1600
1700
1800
1900
2
64. Answers may vary.
Sample: Plot point
(0, 5), then move up 3
and right 4. Plot (4, 8)
and connect the two
points.
78a.
y
2
x
O
2000
1
2
On August 30, 1984, Astronaut Judith A. Resnik
became the second American woman in space,
on the shuttle Discovery’s first voyage. Resnik was
an electrical engineer with a Ph.D. from the
University of Maryland. Prior to her mission, she
helped to design and develop a remote manipulator
system. This required skill in writing linear
equations. Her job during Discovery’s six-day
voyage was to manipulate a robotic arm and to
extend and retract the shuttle’s solar power array.
Resnik died tragically in the Challenger disaster in 1986.
PHSchool.com
x ≠ –2; x ≠ 2
y ≠ 3; y ≠ –3
b. Rectangle; check
students’ work.
c. y ≠ 23 x OR y ≠ –32 x;
explanations may vary.
83. [2]
2
52.
y
1
For: Information about astronauts
Web Code: ate-2032
x
O
53.
y
O
3
1x
1
2
y ≠ –2x
3
y ≠ –23 x – 2
y
3
O
Lesson 6-2 Slope-Intercept Form
51.
5
O y
x
1
3
323
y ≠ 5x – 6
1x
3
slope: 51 2
20 ≠ 2
y-intercept: 3
equation: y ≠ 2x ± 3
[1] correct graph and
minor error in finding
function
5
323