Answers (Lesson 3-1 and Lesson 3-2)

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Lesson 3-2

Answers (Lesson 3-1 and Lesson 3-2)

A4

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3-1 Enrichment

DATE

PERIOD

Spherical Geometry

On a map, longitude and latitude appear to be lines. However, longitude and latitude exist on a sphere rather than on a flat surface. In order to accurately apply geometry to longitude and latitude, we must consider spherical geometry.

The first four axioms in spherical geometry are the same as those in the Euclidean Geometry you have studied. However, in spherical geometry, the meanings of lines and angles are different.

1. A straight line can be drawn between any two points. However, a straight line in spherical geometry is a great circle. A great circle is a circle that goes around the sphere and contains the diameter of the sphere.

2. A finite line segment can be extended infinitely in both directions. A line of infinite length in spherical geometry will go around itself an infinite number of times.

3. A circle can be drawn with any center or radius. So, in spherical geometry, a great circle is both a line and a circle.

4. Right angles can be found on the sphere. Latitude and longitude meet at right angles on a sphere.

The fifth axiom of Euclidean Geometry states that given any straight line and a point not on it, there exists one and only one straight line that passes through that point and never intersects the first line. The fifth axiom is also known as the Parallel Postulate.

Exercises

1. Get a ball. Wrap two rubber bands around the ball to represent two lines (great circles)

on the sphere. How many points of intersection are there? 2

2. Try to draw two lines (great circles) or wrap two rubber bands around a ball that do not

intersect. Is it possible? no

3. Make a conjecture about the number of points of intersection of any two lines (great circles) in spherical geometry.

Two lines (great circles) will always intersect in two points in spherical geometry.

4. Does the fifth axiom, or Parallel Postulate, hold for spherical geometry? Explain.

No, because the Parallel Postulates states that the line will never intersect and that is not possible in spherical geometry because two lines (great circles) always intersect in two points.

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3-2 Study Guide and Intervention

PERIOD

Angles and Parallel Lines Parallel Lines and Angle Pairs When two parallel lines are cut by a transversal,

the following pairs of angles are congruent. ? corresponding angles ? alternate interior angles ? alternate exterior angles

Also, consecutive interior angles are supplementary.

Example In the figure, m2 = 75. Find the measures of the remaining angles.

m1 = 105 m3 = 105 m4 = 75 m5 = 105 m6 = 75 m7 = 105 m8 = 75

1 and 2 form a linear pair. 3 and 2 form a linear pair. 4 and 2 are vertical angles. 5 and 3 are alternate interior angles. 6 and 2 are corresponding angles. 7 and 3 are corresponding angles. 8 and 6 are vertical angles.

p

12 43

m

56 87

n

Exercises

p

q

In the figure, m3 = 102. Find the measure of each angle. Tell which postulate(s) or theorem(s) you used.

12

9 10

43

12 11

m

1. 5 102; Alt. Int. Angles Th. 3. 11 102; Corre. Angles Th.

56

13 14

2. 6 78; Cons. Int. 8 7 16 15

n

Angles Th.

4. 7 102; Corre. Angles Th.

5. 15 102; Corre. Angles Th.

6. 14 78; Cons. Int. Angles Th; Corre. Angles Th.

In the figure, m9 = 80 and m5 = 68. Find the measure of each angle. Tell which postulate(s) or theorem(s) you used.

7. 12 100; Supp. Angles 9. 4 100; Cons Int. Angles Th.

8. 1 80;Corr. Angles Th.

10. 3 80; Att. Int. Angles Th.

12

9 10

4 3 12 11

p

56 87

13 14 16 15

q

w

v

11. 7 68; Vertical Angles Th.

12. 16 112; Vertical Angles Th; Cons. Interior Angles Th.

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Chapter 3

Answers (Lesson 3-2)

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Lesson 3-2

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3-2 Study Guide and Intervention (continued)

Angles and Parallel Lines

Algebra and Angle Measures Algebra can be used to find unknown values in

angles formed by a transversal and parallel lines.

Example If m1 = 3x + 15, m2 = 4x - 5, and m3 = 5y, p

q

find the value of x and y.

p q, so m1 = m2 because they are corresponding angles.

m1 = m2 3x + 15 = 4x - 5 3x + 15 - 3x = 4x - 5 - 3x

15 = x - 5 15 + 5 = x - 5 + 5

20 = x

r s, so m2 = m3 because they are corresponding angles. m2 = m3

75 = 5y - 755 = - 55y 15 = y

1

2

r

4

3

s

Exercises

Find the value of the variable(s) in each figure. Explain your reasoning.

1.

2. 90?

(15x + 30)?

(5x - 5)? (6y - 4)?

(3y + 18)?

10x?

(4x + 10)?

x = 15; y = 19; use corresponding and supplementary angles

x = 6; y = 24; Use consecutive interior angles

3.

(11x + 4)?

(5y + 5)?

4. 3x?

2y?

5x?

(13y - 5)?

x = 11; y = 10; use consecutive interior angles

4y? (5x - 20)?

x = 10; y = 25; Use consecutive interior and alternate interior angles

Find the value of the variable(s) in each figure. Explain your reasoning.

5.

6.

(4z + 6)? x?

2y? z? 2x? 90? x?

106? 2y?

x = 30; y = 15 ; z = 150 use

supplementary, alternate interior,

x = 74; y = 37; z = 25;

and consecutive interior angles

use consecutive interior, corresponding,

and supplementary angles

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3-2 Skills Practice

Angles and Parallel Lines

In the figure, m2 = 70. Find the measure of each angle.

1. 3 70 3. 8 110 5. 4 110

2. 5 110 4. 1 110 6. 6 70

12 34

r

56 78

s

q

In the figure, m7 = 100. Find the measure of each angle.

7. 9 100 9. 8 80 11. 5 100

8. 6 80 10. 2 80 12. 11 100

5 6 1921101

1 4

2 3

m

87

t

u

s

In the figure, m3 = 75 and m10 = 105. Find the measure

of each angle.

13. 2 105 15. 7 105 17. 14 75

14. 5 105 16. 15 105 18. 9 75

3

4 7

8

w

1

2 5

6

x

9113014

11115216

z

y

Find the value of the variable(s) in each figure. Explain your reasoning.

19.

20.

(5x)?

40? (3y - 1)?

(8x - 10)? (6y + 20)? (7x)?

x = 28, y = 47; Use the supplementary angles to find x. Then use alternate exterior angles to find y.

x = 10, y = 15; Use alternate interior angles to find x. Then use supplementary angles to find y.

21.

(9x + 21)?

(11x - 1)? (5y - 5)?

22.

(3x - 3)?

(4y + 4)? 60?

x = 11, y = 13; Use corresponding angles to find x. Then use supplementary angles to find y.

x = 21, y = 29; Use alternate interior angles to find x. Then use supplementary angles to find y.

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Lesson 3-2

Answers (Lesson 3-2)

A6

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3-2 Practice

DATE

PERIOD

Angles and Parallel Lines

In the figure, m2 = 92 and m12 = 74. Find the measure

of each angle. Tell which postulate(s) or theorem(s) you used.

4

1. 10 92; Corr. Th.

2. 8 92; Vert.

36 5

3. 9 88; Corr. Th, Supp s 4. 5 106; Cons.

5. 11 106; Supp.

6. 13 106; Supp.

2 17

m8

12

11 13

10 14 9 15

s

n 16 r

Find the value of the variable(s) in each figure. Explain your reasoning.

7.

(9x + 12)?

3x? (4y - 10)?

8.

(5y - 4)?

3y? (2x + 13)?

x = 14, y = 37; Use Supplementary and alternate exterior angles

Find x. (Hint: Draw an auxiliary line.)

x = 28, y = 23; Use corresponding and supplementary angles

9.

50?

1 100?

10.

62? 1 144?

130

98

11. PROOF Write a paragraph proof of Theorem 3.3.

Given: || m, m || n Prove: 1 12

Sample proof:

k

12 34

It is given that m, so 1 8 by the Alternate

56 78

m

Exterior Angles Theorem. Since it is given that m n,

8 12 by the Corresponding Angles Postulate.

9 10 11 12

n

Therefore, 1 12, since congruence of angles is

transitive.

12. FENCING A diagonal brace strengthens the wire fence and prevents

it from sagging. The brace makes a 50? angle with the wire as shown.

50?

Find the value of the variable. 130

y?

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3-2 Word Problem Practice

PERIOD

Angles and Parallel Lines

1. RAMPS A parking garage ramp rises to connect two horizontal levels of a parking lot. The ramp makes a 10? angle with the horizontal. What is the measure of angle 1 in the figure?

4. PODIUMS A carpenter is building a podium. The side panel of the podium is cut from a rectangular piece of wood.

1

170

Ramp

10?

Level 2 1

Level 1

116?

The rectangle must be sawed along the dashed line in the figure. What is the

measure of angle 1? 64

2. BRIDGES A double decker bridge has two parallel levels connected by a network of diagonal girders. One of the girders makes a 52? angle with the lower level as shown in the figure. What is the measure of angle 1?

1

52?

52

3. CITY ENGINEERING Seventh Avenue runs perpendicular to both 1st and 2nd Streets, which are parallel. However, Maple Avenue makes a 115? angle with 2nd Street. What is the measure of angle 1?

115?

1

65

2nd St. 1st St.

5. SECURITY An important bridge crosses a river at a key location. Because it is so important, robotic security cameras are placed at the locations of the dots in the figure. Each robot can scan x degrees. On the lower bank, it takes 4 robots to cover the full angle from the edge of the river to the bridge. On the upper bank, it takes 5 robots to cover the full angle from the edge of the river to the bridge.

upper bank

lower bank

a. How are the angles that are covered by the robots at the lower and upper banks related? Derive an equation that x satisfies based on this relationship.

They are consecutive interior angles and are supplementary. 4x + 5x = 180

b. How wide is the scanning angle for each robot? What are the angles that the bridge makes with the upper and lower banks?

x = 20; upper bank = 100 and lower bank = 80

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Chapter 3

Answers (Lesson 3-2 and Lesson 3-3)

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3-2 Enrichment

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PERIOD

Vanishing Point

If you look down a road that does not have any curves or bends in it, the sides of the road that are parallel appear to meet at a single point. This is called the vanishing point and has been used in artwork since the 1400s.

The picture below shows a straight road going into the distance. The parallel lines of the left and right sides of the road have been traced to show the vanishing point.

NEXT REST STOP

64 miles

In the following pictures, draw lines to find the vanishing point or points.

1.

2.

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3-3 Study Guide and Intervention

Slopes of Lines

Slope

and (x2,

of

y2)

a

is

Line

given

The slope m of a by the formula m

line containing two points

=

- y2

x2

-

y1 x1

,

where

x1

x2.

with

coordinates

(x1,

y1)

Example Find the slope of each line.

For line p, substitute

- m =

y2 - y1 x2 - x1

(1,

2)

for

(x1,

y1)

and

(-2,

-2)

for

(x2,

y2).

= - --22 -- 21 or -43

For line q, substitute (2, 0) for (x1, y1) and (-3, 2) for (x2, y2).

- m =

y2 - y1 x2 - x1

= - -23--02 or - -25

yp

q (?3, 2)

(1, 2) x

O (2, 0) (?2, ?2)

Exercises

Determine the slope of the line that contains the given points.

1. J(0, 0), K(-2, 8) -4

2. R(-2, -3), S(3, -5)

- -25

3. L(1, -2), N(-6, 3) - -57

4. P(-1, 2), Q(-9, 6)

- -12

5. T(1, -2), U(6, -2) 0

6. V(-2, 10), W(-4, -3) - 123

Find the slope of each line.

7. AB 3

8. CD -2

9. EM undefined 11. EH -25

10. AE 0 12. BM - -12

y B(0, 4)

C(?2, 2) A(?2, ?2)

M(4, 2) x

O D(0, ?2)

E(4, ?2)

H (?1, ?4)

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Chapter 3

Answers (Lesson 3-3)

A8

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3-3

DATE

PERIOD

Study Guide and Intervention (continued)

Slopes of Lines

Parallel and Perpendicular Lines If you examine the slopes of pairs of parallel lines

and the slopes of pairs of perpendicular lines, where neither line in each pair is vertical, you will discover the following properties.

Two lines have the same slope if and only if they are parallel.

Two lines are perpendicular if and only if the product of their slopes is -1.

Example Determine whether AB and CD are parallel, perpendicular, or neither for A(-1, -1), B(1, 5), C(1, 2), D(5, 4). Graph each line to verify your answer.

Find the slope of each line.

slope of AB = - 51 -- ((--11)) = -62 or 3

slope of CD = - 45 -- 21 = -24 = -12

The two lines do not have the same slope, so they are not parallel.

To determine if the lines are perpendicular, find the product of their slopes

( ) 3 -12 = -32 or 1.5

Product of slope for AB and CD

y

Since the product of their slopes is not ?1, the two lines are

not perpendicular.

#

Therefore, there is no relationship between AB and CD. When graphed, the two lines intersect but not at a right angle.

$

0 "

% x

Exercises

Determine whether MN and RS are parallel, perpendicular, or neither. Graph each line to verify your answer.

See students' work

1. M(0, 3), N(2, 4), R(2, 1), S(8, 4)

parallel

2. M(-1, 3), N(0, 5), R(2, 1), S(6, -1)

perpendicular

3. M(-1, 3), N(4, 4), R(3, 1), S(-2, 2)

neither

4. M(0, -3), N(-2, -7), R(2, 1), S(0, -3)

parallel

Graph the line that satisfies each condition. 5. slope = 4, passes through (6, 2)

y (8, 5)

6. passes through H(8, 5), perpendicular to AG with A(-5, 6) and G(-1, -2)

7. passes through C(-2, 5), parallel to LB with L(2, 1) and B(7, 4)

Chapter 3

18

(6, 2)

0

x

(5, -2)

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Slopes of Lines

Determine the slope of the line that contains the given points.

1. S(-1, 2), W(0, 4) 2 3. C(0, 1), D(3, 3) -23

2. G(-2, 5), H(1, -7) - 4 4. J(-5, -2), K(5, -4) - -15

Find the slope of each line.

5.

y

-34

1

6.

y

-2

0

x

/

0

x

5

8

Determine whether AB and MN are parallel, perpendicular, or neither. Graph each line to verify your answer.

See students' graphs.

7. A(0, 3), B(5, -7), M(-6, 7), N(-2, -1)

parallel

9. A(-2, -7), B(4, 2), M(-2, 0), N(2, 6)

parallel

8. A(-1, 4), B(2, -5), M(-3, 2), N(3, 0)

neither

10. A(-4, -8), B(4, -6), M(-3, 5), N(-1, -3)

perpendicular

Graph the line that satisfies each condition.

11. slope = 3, passes through A(0, 1)

y

12. slope = - -32, passes through R(-4, 5)

R(?4, 5) y

A(0, 1)

O

x

O

x

13. passes through Y(3, 0), parallel to DJ with D(-3, 1) and J(3, 3)

y J(3, 3)

D(?3, 1) Y(3, 0)

O

x

14. passes through T(0, -2), perpendicular to CX with C(0, 3) and X(2, -1)

y

C(0, 3)

O T(0, ?2)

x X(2, ?1)

Chapter 3

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Chapter 3

Answers (Lesson 3-3)

6th St. Ford St.

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A9

NAME

3-3 Practice

DATE

PERIOD

Slopes of Lines

Determine the slope of the line that contains the given points.

1. B(-4, 4), R(0, 2) - -12

2. I(-2, -9), P(2, 4) - 143

Find the slope of each line.

3. LM -23

4. GR - -25

L

5. a line parallel to GR

- -25

6. a line perpendicular to PS

- -12

y M

S

OP

x

G

R

Determine whether KM and ST are parallel, perpendicular, or neither. Graph each line to verify your answer.

See students' work

7. K(-1, -8), M(1, 6), S(-2, -6), T(2, 10) 8. K(-5, -2), M(5, 4), S(-3, 6), T(3, -4)

neither

perpendicular

9. K(-4, 10), M(2, -8), S(1, 2), T(4, -7)

parallel

10. K(-3, -7), M(3, -3), S(0, 4), T(6, -5)

perpendicular

Graph the line that satisfies each condition.

11. slope = - -12, contains U(2, -2)

y

12. slope = -43, contains P(-3, -3)

y

O

x

U(2, ?2)

O

x

P(?3, ?3)

13. contains B(-4, 2), parallel to FG with F(0, -3) and G(4, -2)

y

B(?4, 2)

O

x

G(4, ?2)

F(0, ?3)

14. contains Z(-3, 0), perpendicular to EK with E(-2, 4) and K(2, -2)

y E(?2, 4)

Z(?3, 0) O

x K(2, ?2)

15. PROFITS After Take Two began renting DVDs at their video store, business soared. Between 2005 and 2010, profits increased at an average rate of $9000 per year. Total profits in 2010 were $45,000. If profits continue to increase at the same rate, what will the total profit be in 2014? $81,000

Chapter 3

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PERIOD

3-3 Word Problem Practice

Slopes of Lines

1. HIGHWAYS A highway on-ramp rises 15 feet for every 100 horizontal feet traveled. What is the slope of the ramp?

- 230

5. CITY BLOCKS The figure shows a map of part of a city consisting of two pairs of parallel roads. If a coordinate grid is applied to this map, Ford Street would have a slope of -3.

2. DESCENT An airplane descends at a rate of 300 feet for every 5000 horizontal feet that the plane travels. What is the slope of the path of descent? - - 530

3. ROAD TRIP Jenna is driving 400 miles to visit her grandmother. She manages to travel the first 100 miles of her trip in two hours. If she continues at this rate, how long will it take her to drive the remaining distance? 6 hours

N

Clover St.

B St.

a. The intersection of B Street and Ford Street is 150 yards east of the intersection of Ford Street and Clover Street. How many yards south is it?

450 yd

b. What is the slope of 6th Street? Explain.

-3; Ford Street and 6th Street are parallel so they have the same slope.

4. WATER LEVEL Before the rain began, the water in a lake was 268 inches deep. The rain began and after four hours of rain, the lake was 274 inches deep. The rain continued for one more hour at the same intensity. What was the depth of the lake when the rain stopped?

275.5 in.

c. What are the slopes of Clover and B Streets? Explain.

Both have a slope of -13 because both are perpendicular to Ford and 6th, and the slope of a perpendicular is given by the negative reciprocal.

d. The intersection of B Street and 6th Street is 600 yards east of the intersection of B Street and Ford Street. How many yards north is it?

200 yd

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A10

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3-3 Enrichment

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PERIOD

Slopes and Polygons

In coordinate geometry, the slopes of two lines determine if the lines are parallel or perpendicular. This knowledge can be useful when working with polygons.

1. The coordinates of the vertices of a triangle are

A(-6, 4), B(8, 6), and C(4, -4). Graph ABC.

y

2. J, K, and L are midpoints of A-B-, B--C-, and A-C-,

B J

respectively. Find the coordinates of J, K, and L.

A

Draw JKL.

J(1, 5), K(6, 1), L(-1, 0)

K

LO

x

3. Which segments appear to be parallel?

A-B- and L-K-, B-C- and J-L-, A-C- and J-K-

C

4. Show that the segments named in Exercise 3 are parallel by finding the slopes of all six segments.

A-B-: -17; L-K-: -17; B-C-: -52; J-L-: -52; A-C-: --45; J-K-: --45

The coordinates of the vertices of right PQR are given. Find the slope of each side of the triangle. Then name the hypotenuse.

5. P(5, 1), Q(1, -1), R(-2, 5)

slope slope

of of

P--Q- = Q--R- =

-12 - 2

slope of P-R- = --47 hypotenuse: P-R-

6. P(-2, -3), Q(5, 1), R(2, 3)

slope of P--Q- = slope of Q--R- =

--47-23

slope of P-R- =

hypotenuse: P-Q-

-32

The coordinates of quadrilateral PQRS are given. Graph quadrilateral PQRS and find the slopes of the diagonals. State whether the diagonals are perpendicular.

7. P(-2, 6), Q(4, 0), R(1, -4), S(-5, 2)

P

y

S

Q

O

x

R

P-R-: - - 130; S-Q-: - -29; no

Chapter 3

8. P(0, 6), Q(3, 0), R(-4, -2), S(-5, 4)

y P

S

O

Qx

R

P-R-: 2; S-Q-: - -12; yes 22

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3-3 Spreadsheet Activity

Slopes of Lines

You can use a spreadsheet to investigate the slope of a line.

PERIOD

Example 1 Use a spreadsheet to find the slope of a line that contains the

points (-2, 3) and (4, 1).

Step 1 Use the first cell of the spreadsheet for the x value of the first point. Use cell B1

for the y value of the first point. Use cell C1 for the x value of the second point and

use cell D1 for the y value of the second point.

Step 2 In cell E1, enter an equals sign followed by the expression for the numerator of the

slope, which is D1 - B1. Then press ENTER to return the numerator of the slope

of the line.

Step 3 In cell F1, enter an equals sign

followed by the expression for the

denominator of the slope, which is

ABCD E F

C1 - A1. Then press ENTER to return the denominator of the slope.

1 2 3

2 1

0

3

4

2 3

1

2

1 2

6

6

4 2

2

1

2

The numerator of the slope is -2 and the

4

denominator is 6. So,the slope is - -26 or - -13.

Sheet 1 Sheet 2 Sheet 3

Example 2 Use a spreadsheet to determine whether PQ and UV are parallel, perpendicular, or neither for P(-1, 2), Q(-3, 6), U(0, 1), and V(2, 2).

Step 1 Step 2

Enter the ordered pairs for PQ in row 2 and the ordered pairs for UV in row 3 as above. With cell E1 selected, click on the bottom right corner of cell E1 and drag it to E3. This returns the numerators of the slopes. With cell F1 selected, click on the bottom right corner of cell F1 and drag it to F3. This returns the denominators of the slopes.

For PQ, the numerator of the slope is 4 and the denominator is -2. So, the slope

is - -42 or -2. For UV, the numerator of the slope is 1 and the denominator is 2. So, the slope is -12. Since the product of the slopes is -1, the lines are perpendicular.

Exercises

Use a spreadsheet to find the slopes of the lines that contain the given points.

1. (2, 4), (1, 7)

2. (-2, 8), (3, -5)

3. (0, 4), (7, 0)

4. (3, 5), (-1, 9)

5. (3, -1), (9, -6)

6. (-2, 5), (-7, -2)

Use a spreadsheet to determine whether PQ and UV are parallel, perpendicular, or neither.

7. P(22, 3), Q(3, 1), U(0, 3), and V(5, 5)

8. P(3, 5), Q(1, 22), U(23, 24), and V(21, 3)

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Chapter 3

Answers (Lesson 3-4)

A11

NAME

DATE

PERIOD

3-4 Study Guide and Intervention

Equations of Lines

Write Equations of Lines You can write an equation of a line if you are given any of

the following: ? the slope and the y-intercept, ? the slope and the coordinates of a point on the line, or ? the coordinates of two points on the line.

If m is the slope of a line, b is its y-intercept, and (x1, y1) is a point on the line, then: ? the slope-intercept form of the equation is y = mx + b, ? the point-slope form of the equation is y - y1 = m(x - x1).

Example 1 Write an equation in slope-intercept form of the line with slope -2 and y-intercept 4.

y = mx + b

Slope-intercept form

y = -2x + 4

m = -2, b = 4

The slope-intercept form of the equation of the line is y = -2x + 4.

Example 2 Write an equation in

point-slope form of the line with slope --34 that contains (8, 1).

y - y1 = m(x - x1)

Point-slope form

y - 1 = --34 (x - 8)

m = --34, (x1, y1) = (8, 1)

The point-slope form of the equation of the

line is y - 1 = --34 (x - 8).

Exercises

Write an equation in slope-intercept form of the line having the given slope and

y-intercept or given points. Then graph the line.

See students' work

1. m: 2, b: -3

y = 2x - 3

3. m: -14, b: 5

2. m: - -12, b: 4

y = - -12 x + 4

4. m: 0, b: -2

y = -14x + 5

5. m: - -53, (0 , -13)

y = -2

6. m: -3, (1,-11)

y = - -53x + -13

y = -3x - 8

Write an equation in point-slope form of the line having the given slope that

contains the given point. Then graph the line.

See students' work

7. m = -12, (3, -1)

y + 1 = -12(x - 3)

9. m = -1, (-1, 3)

y - 3 = -(x + 1)

11. m = - -52, (0, -3)

y + 3 = - -52x

8. m = -2, (4, -2)

y + 2 = -2(x - 4)

10. m = -14, (-3, -2)

y + 2 = - -14(x + 3)

12. m = 0, (-2, 5)

y - 5 = 0

Chapter 3

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Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME

DATE

PERIOD

3-4 Study Guide and Intervention (continued)

Equations of Lines

Write Equations to Solve Problems Many real-world situations can be modeled

using linear equations.

Example Donna offers computer services to small companies in her city. She charges $55 per month for maintaining a web site and $45 per hour for each service call.

a. Write an equation to represent the total monthly cost, C, for maintaining a web site and for h hours of service calls.

For each hour, the cost increases $45. So the rate of change, or slope, is 45. The y-intercept is located where there are 0 hours, or $55.

b. Donna may change her costs to represent them by the equation C = 25h + 125, where $125 is the fixed monthly fee for a web site and the cost per hour is $25. Compare her new plan to the old one if a company has 5 -12 hours of service calls. Under which plan would Donna earn more?

First plan

For 5 -12 hours of service Donna would earn

( ) C = 45h + 55 = 45 5 -12 + 55

= 247.5 + 55 or $302.50

C = mh + b

Second Plan

= 45h + 55

For 5 -12 hours of service Donna would earn C = 25h + 125 = 25(5.5) + 125

= 137.5 + 125 or $262.50

Donna would earn more with the first plan.

Exercises

For Exercises 1?4, use the following information.

Jerri's current satellite television service charges a flat rate of $34.95 per month for the basic channels and an additional $10 per month for each premium channel. A competing satellite television service charges a flat rate of $39.99 per month for the basic channels and an additional $8 per month for each premium channel.

1. Write an equation in slope-intercept form that models the total monthly cost for each satellite service, where p is the number of premium channels.

Current service: C = 10p + 34.95

Competing service: C = 8p + 39.99

2. If Jerri wants to include three premium channels in her package, which service would be less, her current service or the competing service?

competing service

3. A third satellite company charges a flat rate of $69 for all channels, including the premium channels. If Jerri wants to add a fourth premium channel, which service would be least expensive?

the third company

4. Write a description of how the fee for the

number of premium channels is reflected

in the equation. The fee for the number of premium channels represents the rate of change, or slope, of the equation.

Chapter 3

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Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 3-4

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Answers

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