Evaluate: Homework and Practice

Elaborate 11. What is a solution of a linear equation in two variables?

12. What type of function has a graph with a series of unconnected points?

13. Essential Question Check-In What is the standard form for a linear equation?

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Determine if the equation is linear. If so, graph the function. 1.

2x + y = 4

8

y

4 x -8

-4

x

© Houghton Mifflin Harcourt Publishing Company

4

-4

8

-8

y 2.

0

2x 2 + y = 6

8

y

4 x -8

-4

0

4

-4

8

-8

3.

y _ 2 +_ _ =3 x 4 2

8

y

4 x -8

-4

0 -4

4

8

-8 Module 5

205

Lesson 1

4.

3x + 4y = 8

y

8 4

x -8

-4

x

4

-4

8

-8

y 5.

0

x + y2 = 1

8

y

4 x -8

-4

0

4

-4

8

-8

6.

x+y=1

8

y

4 x -8

x

-4

0 -4

4

8

-8

y State whether each function is discrete or continuous. The number of basketballs manufactured per day 8.

9.

The number of bulls eyes scored for each hour of practice

11. y = 35x 1, where x is distance and y is height

Module 5

© Houghton Mifflin Harcourt Publishing Company

7.

y x = _ , where x is the number of hours and 4 y is the miles walked

10. y = 4 4 x, where x is the time and y is gallons of water

12. The amount of boxes shipped per shift

206

Lesson 1

Graph each function and give its domain and range. 13. Hans opens a new video game store and pays the 14. Peter opens a new bookstore and pays the book gaming companies $5.00 for each video game he publisher $3.00 for each book he buys from them. buys from them. The amount Hans pays is given The amount Peter pays is given by ƒ(x) = 3x, by ƒ(x) = 5x, where x is the number of video where x is the number of books purchased. games purchased.

Video Game Purchases 25

Book Purchases

y

12 Cost ($)

20 Cost ($)

y

15

15 10

9 6 3

5

x

x 0

0

1 2 3 4 5 Number of video games

1

2 3 4 Number of books

5

15. Steve opens a jewelry shop and makes $15.00 16. Anna owns an airline and pays the airport $35.00 profit for each piece of jewelry sold. The amount for each ticket sold. The amount Anna pays is Steve makes is given by ƒ(x) = 15x, where x is the given by ƒ(x) = 35x, where x is the number of number of pieces of jewelry sold. tickets sold.

Jewelry Sales 175

60

y

140 Cost ($)

Profit ($)

© Houghton Mifflin Harcourt Publishing Company

75

Airplane Ticket Sales

y

45 30 15

105 70 35

x 0

Module 5

1

2 3 4 Number of pieces

x

5

0

207

1 2 3 4 Number of tickets

5

Lesson 1

x y

(9, 765)

765

(7, 595)

85

x

595 425

y=

Fill in the table using the data points from the graph. Determine whether x and y have constant change between consecutive terms and whether they are in a linear function.

y Number of miles

17. A hot air balloon can travel up to 85 mph. If the balloon travels continuously at this speed, y = 85x gives the number of miles y that the hot air balloon would travel in x hours.

(3, 255)

255

(1, 85)

85 1

18. State whether each function is in standard form. a. 3x + y = 8 c.

x 2 + y = 11

e. x + 4y = 12

x

3 5 7 9 Number of hours

19. Physics A physicist working in a large laboratory has found that light particles traveling in a particle accelerator increase velocity in a manner that can be described by the linear function -4x + 3y = 15, where x is time and y is velocity in kilometers per hour. Use this function to determine when a certain particle will reach 30 km/hr.

b. x - y = 15z d. 3xy + y 2 = 4 f.

(5, 425)

5x + 24y = 544

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208

Lesson 1