Skills Practice Skills Practice for Lesson 1.1

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1 Skills Practice

Skills Practice for Lesson 1.1

Name _____________________________________________ Date ____________________

Tanks a Lot

Introduction to Linear Functions

Vocabulary

Define each term in your own words.

1. function

A function is a relation that maps each value of the independent variable to exactly one value of the dependent variable.

2. linear function

A linear function is a function that has a constant rate of change and a graph that is a non-vertical straight line.

3. independent variable

An independent variable is a variable assigned to an independent quantity.

4. dependent variable

A dependent variable is a variable assigned to a dependent quantity.

5. variable

A variable is a letter or symbol that represents a quantity.

Problem Set

Determine the independent quantity and the dependent quantity in each example.

6. A car is traveling at a rate of sixty miles per hour for several hours.

independent quantity: time in hours dependent quantity: distance in miles

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7. Sharon is growing at a rate of two inches per year.

independent quantity: time in years dependent quantity: height in inches

8. The area of a square floor is the product of the length of two of its sides.

independent quantity: side length of floor dependent quantity: area of floor

9. The perimeter of a square is the sum of the length of all four of its sides.

independent quantity: side length of square dependent quantity: perimeter of square

10. The length of a video file in minutes relates to the size of the file in bytes.

independent quantity: length of a video file in minutes dependent quantity: size of the file in bytes

11. The total weight of a bag of apples in pounds relates to the number of apples in the bag.

independent quantity: number of apples

dependent quantity: total weight of bag in pounds

Define a variable to represent each of the quantities. Then write an equation that shows the relationship between the two variables.

12. A runner travels 4 miles per hour. Write an equation to show the relationship between the total distance the runner travels and the time.

Let t represent the amount of time in hours.

Let d represent the distance the runner travels in miles.

d 4t

13. Each DVD at an electronics store costs $12.50. Write an equation to show the relationship between the total cost when purchasing DVDs and the number of DVDs.

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Name _____________________________________________ Date ____________________

1

14. To make one solar panel, a company uses two kilograms of silicon. The company has 100 kilograms of silicon. Write an equation to show the relationship between the amount of silicon remaining and the number of solar panels made.

Let s represent the amount of silicon remaining in kilograms.

Let n represent the number of solar panels made.

s 100 2n

15. A bowling ball company uses seven pounds of resin to make one seven-pound bowling ball. They have a total of 490 pounds of resin. Write an equation to show the relationship between the amount of resin remaining and the number of seven-pound bowling

balls made.

Let r represent the amount of resin remaining in pounds.

Let b represent the number of bowling balls made.

r 490 7b

16. Julia opens a bank account and deposits $500 into the account. Each month, she deposits $50 into the account. Write an equation to show the relationship between the total amount of money in her bank account and the number of months since she opened the account.

Let m represent the number of months since Julia opened the account.

Let d represent the total amount in the account in dollars.

d 50m 500

17. A water tower contains 15,000 gallons of water. Each week, 2500 gallons of water are used and 1000 gallons of water are added. Write an equation to show the relationship between the total amount of water remaining in the water tower and the number of weeks that have elapsed.

Let w represent the number of weeks that have elapsed.

Let g represent the amount of water remaining in the water tower in gallons.

g 15,000 1500w

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Graph each linear function.

18. y 2 x 1 19. y 3x 2

20. y 1 ^__2 x 2 21. y 2 ^__3 x 1 ^__2

22. y 4x 5 ^__4 23. y 2x 7 ^__3

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

y = 2x – 1

1 2 3 4

–1 –2 –3 –4 y

1 3

y = 3x + 2

4 2 –3

–4 –2 –1 0 x

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1

x y = 1x + 2

–2

0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y =2x –

3 1

2

0

1 2 3 4

–1 y

1 2 3 4

–3

–4 –2 –1 x

y = –4x – 54

0

1 2 3 4

–1 y

1 2 3 4

–3

–4 –2 –1 0 x

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Name _____________________________________________ Date ____________________

1

Use the given information to answer each question.

24. The distance, d, in miles that a plane travels can be modeled by the equation d 550t, where t represents the time in hours. If the plane travels for 7 hours, how far will it go?

d 550t d 550(7) d 3850

The plane will travel 3850 miles in 7 hours.

25. The distance, d, in feet that a fly travels can be modeled by the equation d 5t, where t represents the time in seconds. If the fly travels for 30 seconds, how far will it have gone?

d 5t d 5(30) d 150

The fly will travel 150 feet in 30 seconds.

26. The equation w 1,000,000 20m shows the amount of water, w, in gallons remaining in a water tower, where m represents the number of minutes that have passed. When will there be 750,000 gallons of water in the water tower?

w 20m 1,000,000 750,000 20m 1,000,000

250,000 20m 12,500 m

After 12,500 minutes, or 208 hours and 20 minutes, there will be 750,000 gallons of water in the tower.

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27. The equation a 1750 50t shows the amount of money, a, in dollars remaining in a bank account where t represents the time in weeks. When will the balance in the account be $1000?

a 50t 1750 1000 50t 1750

750 50t 15 t

After 15 weeks, the balance in the bank account will be $1000.

28. A ticket seller’s weekly earning, s, in dollars can be modeled by the equation s 0.10t 350, where t represents the number of tickets he sells. How many tickets will the ticket seller have to sell to make $440 that week?

s 0.10t 350 440 0.10t 350

90 0.10t 900 t

The ticket seller will have to sell 900 tickets that week to make $440.

29. The total number of computers, c, that a company can manufacture can be modeled by the equation c 1 ^___50 s 250, where s represents the number of screws that they need to order. How many screws will they need to order so that they can manufacture 525 computers?

c 1 ^___50 s 250 525 1 ^___50 s 250 275 1 ^___

50 s 13,750 s

The company needs to order 13,750 screws to manufacture 525 computers.

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1 Skills Practice

Name _____________________________________________ Date ____________________

Calculating Answers

Solving Linear Equations and Linear Inequalities

in One Variable

Vocabulary

Write the term that best completes each statement.

1. The solution of an inequality can be graphed on a(n) number line . 2. Adding, subtracting, multiplying, and distributing are all examples of

simplifications that can be used to solve an equation.

3. Addition, subtraction, multiplication, and division are the four

basic transformations that can be applied to both sides of a linear equation to solve the equation.

4. A(n) inequality is a statement that compares two expressions.

Problem Set

Indicate which transformation(s) are needed to solve each equation.

5. x 1 4 6. x 3 2

Add 1 to both sides. Subtract 3 from both sides.

7. 2x 4 8. x __

4 7

Divide both sides by 2. Multiply both sides by 4.

9. 3x 2 8 10. x __

2 5 15

First, subtract 2 from both sides. First, add 5 to both sides.

Then, divide both sides by 3. Then, multiply both sides by 2.

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1

S olve each equation.

11. x 3 10 12. 3 x 1

x 3 3 10 3 3 3 x 1 3

x 7 x 4

13. 2x 6 10 14. 3x 9 27

2 x 6 6 10 6 3x 9 9 27 9

2 x 16 3x 18

2 x ___

2 16 ^___2 3x ___

3 18 ^___3

x 8 x 6

15. x __

2 3 1 16. x ^__3 2 4 x __

2 3 3 1 3 x ^__3 2 2 4 2 x __

2 2 x ^__3 6

2

(

^x^__2

)

²⁽²⁾³

(

^x^__3

)

³⁽⁶⁾

x 4 x 18

17. 2 ^__3 x 3 1 18. 3 __

5 x 4 8 2 ^__3 x 3 3 1 3 3 __

5 x 4 4 8 4 2 ^__3 x 4 3 __

5 x 12 3

(

²^__3 x

)

³⁽⁴⁾ ⁵

(

³^__5 x

)

⁵⁽¹²⁾

2 x 12 3x 60

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Name _____________________________________________ Date ____________________

1

19. 2 x 15 5 3x 20. 4x 3x 9 2 x

2 x 3x 15 5 3x 3x 4x 3x 2 x 9 2x 2x 5x 15 5 3x 9

5x 15 15 5 15 3x ___

3 9 ^__3 5x 10 x 3 5x ___

5 10 ^___5 x 2

S olve each inequality. Graph the solution on a number line.

21. 3x 2 ⬍ 8 22. 2x 5 ⬎ 7

3x 2 2 ⬍ 8 2 2 x 5 5 ⬎ 7 5

3x ⬍ 6 2 x ⬎ 12

3x ___

3 ⬍ 6 ^__3 2 x ___

2 ⬎ 12 ^___2

x ⬍ 2 x ⬎ 6

23. 4x 3 ⱕ 13 24. 2 3x ⱖ 11

4x 3 3 ⱕ 13 3 2 2 3x ⱖ 11 2 4x ⱕ 16 3x ⱖ 9 4x ____

4 ⱖ 16 ^_____4 3x ____

3 ⱕ 9 ^___3 x ⱖ 4 x ⱕ 3

25. 2x 3 5 26. x 4 13

2 x 3 3 ⫽ 5 3 x 4 4 ⫽ 13 4

2 x ⫽ 8 x ⫽ 17

2 x ___

2 ⫽ 8 ^__2 x ⫽ 17 x ⫽ 4

1 2 3 4 5

–3 –4

–5 –2 –1 0 –10–8 –6 –4 –2 0 2 4 6 8 10

1 2 3 4 5

–3 –4

–5 –2 –1 0 –5 –4 –3 –2 –1 0 1 2 3 4 5

12 14 16 18 20 4

2

0 6 8 10

1 2 3 4 5

–3 –4

–5 –2 –1 0

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1

27. 2( x 3) ⱖ 5 28. 4 ⱖ 3(2x 5)

2(_{________}x 3)

2 ⱖ 5 ^__2 4 ___

3 ⱕ ___________ 3(2 x 5)

3 x 3 ⱖ 5 ^__2 4 ^__3 ⱕ 2 x 5 x 3 3 ⱖ 5 ^__2 3 4 ^__3 5 ⱕ 2 x 5 5 x ⱖ 1 ^__2 19 ^___3 ⱕ 2 x

1 __

2

(

¹⁹^___3

)

^{ⱕ 1}^__2 (2x)

19 ^___6 ⱕ x

x ⱖ 19 ^___6

29. x ^__2 3 4 30. 2 __

3 x 4 10 x ^__2 3 3 ⬍ 4 3 2 __

3 x 4 4 ⬎ 10 4 x ^__2 ⬍ 1 2 __

3 x ⬎ 14 2

(

^x^__2

)

^{⬎ 2(1)} ³

(

²^__3 x

)

^{⬎ 3(14)}

x ⬎ 2 2 x ⬎ 42

2 __

2 x ⬎ 42 ^___2

x ⬎ 21

1 2 3 4 5

–3 –4

–5 –2 –1 0 –5 –4 –3 –2 –1 0 1 2 3 4 5

15 20 25

5

0 10

1 2 3 4 5

–3 –4

–5 –2 –1 0

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1 Skills Practice

Name _____________________________________________ Date ____________________

Running a 10K

Slope-Intercept Form of Linear Functions

Vocabulary

Determine each of the following for the linear function 2 x 3y 6.

1. slope 2. y-intercept

2 ^__3 y 2

3. slope-intercept form 4. x-intercept

y 2 ^__3 x 2 x 3

Problem Set

Identify the slope of each linear function.

5. y 2 x 3 6. y 3x 4

The slope is 2. The slope is 3.

7. y 2 ^__3 x 1 ^__2 8. y 5 ^__2 x 2 ^__5 The slope is 2 ^__3 . The slope is 5 __

2 .

Identify the y-intercept of each linear function.

9. y 5x 2 10. y x 3

The y-intercept is 2. The y-intercept is 3.

11. y 2 ^__3 x 1 ^__2 12. y 3 ^__2 x 3 ^__2

The y-intercept is 1 ^__2 . The y-intercept is 3 __

2 .

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1

Write a linear equation in slope-intercept form for each situation.

13. Louise opens a bank account and deposits $250. Every month she deposits $50 into her account. Write an equation to represent the amount she has in her account after x months.

y 50x 250

14. Erin opens a bank account and deposits $350. Every month she withdraws $25 from her account. Write an equation to represent the amount she has in her account after x months.

y 25x 350

15. A computer is downloading a 100-megabyte program file. It downloads the program at a rate of 5 megabytes per minute. Write an equation to represent the number of megabytes left to download after x minutes.

y 5x 100

16. Marco has 20 gigabytes of computer programs on his computer. Every month he adds 1.5 gigabytes of programs to his computer. Write an equation to represent the number of gigabytes of programs he has on his computer after x months.

y 1.5x 20

Calculate the slope and y-intercept for each function.

17. A linear function passes through the points (0, 0) and (4, 8).

The y-intercept is 0.

m y_______ ² y1

x₂ x1

8 0 ^______4 0 8 ^__4 2 The slope is 2.

18. A linear function passes through the points (0, 0) and (3, 27).

The y-intercept is 0.

m y_______ x₂₂ y x11

27 0 ^________3 0 27 ^_____3 9 The slope is 9.

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Name _____________________________________________ Date ____________________

1

19. A linear function passes through the points (4, 9) and (3, 5).

m y_______ x₂₂ y x11

5 9 ^________3 (4) 4 ^__7 The slope is 4 ^__7 .

y mx b 5 4 ^__7 (3) b 5 12 ^___7 b

b 47 ^___7

The y-intercept is 47 ___

7 .

m y_______ ₂ y1

x₂ x1

10 __________ (2) 3 (5) 12 ^___8 3 ^__2 The slope is 3 __

2 . y mx b 10 3 ^__2 (3) b 10 9 ^__2 b

b 11 ^___2

The y-intercept is 11 ___

2 .

21. A linear function passes through the points (3, 0) and (4, 2).

m y_______ x₂₂ y x11

2 0 ^______4 3 2 ^__1 2 The slope is 2.

y mx b 0 2(3) b 0 6 b

b 6

The y-intercept is 6.

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1

m y_______ x₂₂ y x11

__________ 0 (6)

4 (2) 6 ^___2 3 The slope is 3.

y mx b 0 3(4) b 0 12 b

b 12

The y-intercept is 12.

Graph each linear function using its slope and y-intercept.

23. y x 2 24. y 2x 3

Slope 1 Slope 2

y-intercept 2 y-intercept 3

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = x + 2

0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = –2x – 3 0

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Name _____________________________________________ Date ____________________

1

25. y 1 ^__2 x 1 26. y 3 ^__2 x 1 Slope 1 ^__2 Slope 3 ^__2

27. y 4 28. y 3

Slope 0 Slope 0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = – 12x – 1

0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = 3 2x + 1

0

y = 4

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

y = –3 1

2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

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1

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1 Skills Practice

Name _____________________________________________ Date ____________________

Pump It Up

Standard Form of Linear Functions

Vocabulary

Give an example of each key term.

1. standard form of a linear equation 2x 3y 12

2. slope-intercept form of a linear equation y 3x 4

Problem Set

For each linear equation written in standard form, calculate the x- and y-intercepts. Use the intercepts to graph the equation.

3. x y 3 4. x y 2

x 0 3 0 y 3 x 0 2 0 y 2 x 3 y 3 x 2 y 2 x-intercept 3; y-intercept 3 x-intercept 2; y-intercept 2

1 2 3 (0,3)

(3,0) 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

1 2 3

(0,–2) (–2,0)

4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

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1

5. 2x 3y 6 6. x 2y 4

2x 6 3y 6 x 4 2y 4 x 3 y 2 y 2 x-intercept 3; y-intercept 2 x-intercept 4; y-intercept 2

7. 2x 5y 10 8. 3x 4y 12

2x 10 5y 10 3x 12 4y 12 x 5 y 2 x 4 y 3 x-intercept 5; y-intercept 2 x-intercept 4; y-intercept 3

1 2 3

(3,0) (0,2) 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

1 2 3

(4,0) (0,2)

4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1

x 0

1 2 3

(–5,0)

(2,0) 4

–1 –2 –3 –4 y

1 2 3

–3 –2 –4

–5 –1

x 0

1 2 3

(4,0)

(0,–3) 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

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Name _____________________________________________ Date ____________________

1

9. 2 x y 3 10. x 3y 5

2 x 3 y 3 x 5 3y 5 x 3 ^__2 y 3 x 5 y 5 ^__3 x-intercept 3 ^__2 ; y-intercept 3 x-intercept 5; y-intercept 5 ^__3

Rewrite each linear equation in slope-intercept form.

11. x y 2 12. x y 1

y x 2 y x 1

13. 2x y 5 14. 2 x y 3

y 2 x 5 y 2 x 3 y 2 x 5

15. 2x 3y 12 16. 5x 3y 15

3y 2 x 12 3y 5x 15

y 2 ^__3 x 4 y 5 ^__3 x 5

17. 3x 2y 1 18. x 5y 10

2y 3x 1 5y x 10

y 3 ^__2 x 1 ^__2 y 1 ^__5 x 2

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

(

³₂^,⁰

)

(0,–3) 0

1 2 3 4

–1 –2 –3 –4 y

1 2

–5

–6 –4 –3 –2 –1 x

(–5,0)

(

⁰^,⁵₃

)

0

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1

Rewrite each linear equation in standard form.

19. y 2 x 3 20. y 4x 5

2 x y 3 4x y 5

21. y 1 ^__3 x 4 22. y 2 ^__3 x 1

3y x 12 3y 2 x 3

x 3y 12 2 x 3y 3

23. y 5 ^__4 x 1 ^__6 24. y 4 ^___15 x 5 ^__9

12y 15x 2 45y 12 x 25

15x 12y 2 12 x 45y 25

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1 Skills Practice

Name _____________________________________________ Date ____________________

Shifts and Flips

Basic Functions and Linear Transformations

Vocabulary

Write the term that best completes each statement.

1. A function undergoes a(n) dilation when it is stretched or shrunk.

2. A(n) line of reflection is a line in which a function is flipped so that it mirrors itself.

3. A(n) reflection is a transformation in which a function is flipped over a given line.

4. The function y x is the basic function of the function y 2 x 3.

Problem Set

Indicate the algebraic transformation which was performed on the basic function to result in each transformed function.

5. y x 2 6. y x 1

Add 2. Subtract 1.

7. y 4x 8. y 1 ^__5 x

Multiply by 4. Multiply by 1 __

5 .

Indicate the graphical transformation(s) which were performed on the basic function to result in each transformed function.

9. y x 3

Move the graph down 3 units.

10. y x 1

Move the graph up 1 unit.

11. y 2 x 3

Dilate by a factor of 2, then shift up 3 units.

12. y 3x 4

Dilate by a factor of 3, reflect about the x-axis, and shift down 4 units.

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1

13. y 1 ^__2 x 3

Dilate by a factor of 1 __

2 , reflect about the x-axis, and shift up 3 units.

14. y 5 ^__3 x 4

Dilate by a factor of 5 __

3 , and shift up 4 units.

Graph each set of equations on the same grid. Compare the graphs of the lines. Then determine whether the graphs of the lines are parallel, perpendicular, or neither.

15. y x 3 and y x 1 16. y 2 x and y 4x

The first graph is shifted two units up The second graph is twice as steep as from the second graph. The lines the first graph. The lines are

are parallel. neither parallel nor perpendicular.

1 2

3 y = x + 1

y = x + 3

4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

1 2

3 y = 2x

y = 4x 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –10 x

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Name _____________________________________________ Date ____________________

1

17. y x and y x 2 18. y 1 ^__2 x 2 and y 2x 3

The first graph is reflected about the x-axis The second graph is 4 times as steep as and shifted down 2 units from the second the first graph, reflected about the x-axis, graph. The lines are perpendicular. and shifted up 1 unit from the first graph.

The lines are perpendicular.

19. y 2 ^__3 x 2 and y 2 ^__3 x 2 20. y 1 ^__4 x 3 and y 1 ^__2 x 1

The first graph is shifted down 4 units The second graph is twice as steep as from the second graph. The lines the first graph and shifted down 4 units are parallel. from the first graph. The lines are

neither parallel nor perpendicular.

1 2

3 y = x + 2

y = –x 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 0 x

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y =2x + 2 3

y =2x – 2 3 0

1 2 3

y = –2x + 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y =1x + 2 2

0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y =1x + 3 4

y =1x – 1 2 0

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1

21. y 1 ^__

5 x and y 5x 22. y x 2 and y x 2

The second graph is 25 times as steep The first graph is reflected about the as the first graph and reflected about x-axis. The lines are perpendicular.

the x-axis. The lines are perpendicular.

23. y 2 x 1 and y 2 x 3. 24. y 0 and y 3

The first graph is shifted up 4 units from The second graph is shifted up 3 units the second graph. The lines are parallel. from the first graph. The lines are

parallel.

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = 5x

y = 1x –5 0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = –2x + 1

y = –2x – 3 0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = x – 2

y = –x – 2 0

1 2 3 4

–1 –2 –3 –4 y

1 2 3 4

–3

–4 –2 –1 x

y = 0 y = 3

0

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1 Skills Practice

Name _____________________________________________ Date ____________________

Inventory and Sand

Determining the Equations of Linear Functions

Vocabulary

Identify the similarities and differences between each pair of key terms.

1. point-slope form and two-point form

Both are forms of linear equations that use a point on a line and the slope of a line. If you divide both sides of a linear function in point-slope form by x x1, then the linear function will be in two-point form.

2. parallel lines and perpendicular lines

Parallel lines never intersect and their slopes are the same. Perpendicular lines intersect and their slopes are negative reciprocals.

Problem Set

Determine the slope-intercept form of the equation of each line.

3. Slope 2 and y-intercept 3 4. Slope 4 and y-intercept 10 y 2 x 3 y 4x 10

5. Slope 1 and y-intercept 4 6. Slope 1 and y-intercept 12 y x 4 y x 12

Determine the slope-intercept form of the equation of each line.

7. Slope 5 and the line passes 8. Slope 10 and the line passes through the point (2, 3) through the point (3, 5)

y 3 5( x 2) y 5 10( x 3) y 3 5x 10 y 5 10x 30 y 5x 13 y 10x 25

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1

9. Slope 7 and the line passes through 10. Slope 3 and the line passes the point (1, 4) through the point (5, 6)

y (4) 7( x 1) y (6) 3( x 5) y 4 7x 7 y 6 3x 15 y 7x 11 y 3x 9

Determine the slope-intercept form of the equation of the line passing through each pair of points.

11. (1, 2) and (5, 3) 12. (2, 6) and (5, 8) m 3 2 ^______5 1 1 ^__4

y 3 1 ^__4 ( x 5) y 1 ^__4 x 5 ^__4 3 y 1 ^__4 x 7 ^__4

m 8 6 ^______5 2 2 ^__3 y 8 2 ^__3 ( x 5) y 2 ^__3 x 10 ^___3 8 y 2 ^__3 x 14 ^___3

13. (2, 5) and (4, 3) 14. (1, 7) and (5, 3) m 3 5 ^________4 (2) 8 ^__6 4 ^__3

y 5 4 ^__3 ( x 2) y 4 ^__3 x 8 ^__3 5 y 4 ^__3 x 7 ^__3

m __________ 3 (7) 5 1 4 ^__4 1 y 3 x 5

y x 8

15. (0, 3) and (1, 3) 16. (2, 4) and (3, 4)

m 3 3 ^______1 0 0 ^__1 0 y 3 0

y 3

m 4 4 ^______3 2 0 ^__1 0 y 4 0

y 4

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Name _____________________________________________ Date ____________________

1

Determine the slope-intercept form of the equation of each line, given the equation of a line parallel to the line and a point on the line.

17. y 3x 2, (1, 4) 18. y 5x 6, (3, 5)

4 3(1) b 5 5(3) b

1 b 5 15 b

y 3x 1 10 b

y 5x 10

19. y 2 x 3, (2, 6) 20. y 4x 1, (3, 4)

6 2(2) b 4 4(3) b

6 4 b 4 12 b

2 b 8 b

y 2x 2 y 4x 8 21. y 1 ^__3 x 11, (6, 5) 22. y __ 3

2 x 10, (4, 3)

5 1 ^__3 (6) b 3 3 ^__2 (4) b

5 2 b 3 6 b

3 b 3 b

y 1 ^__3 x 3 y 3 ^__2 x 3

Determine the slope-intercept form of the equation of each line, given the equation of a line perpendicular to the line and a point on the line.

23. y 3x 1, (2, 4) 24. y 4x 3, (1, 1)

m₁ 1 ^___m₂ 1 ^__3 y 4 1 ^__3 ( x 2) y 1 ^__3 x 2 ^__3 4 y 1 ^__3 x 14 ^___3

m₁ 1 ^___m₂ 1 ^__4 y 1 1 ^__4 ( x 1) y 1 ^__4 x 1 ^__4 1 y 1 ^__4 x 5 ^__4

(28)

1

25. y 1 ^__3 x 2, (3, 2) 26. y __ 3

4 x 9, (5, 1) m₁ 1 ^___m₂ 3

y (2) 3( x 3) y 3x 9 2 y 3x 7

m₁ 1 ^___m₂ 4 ^__3 y 1 4 ^__3 ( x (5)) y 4 ^__3 x 20 ^___3 1 y 4 ^__3 x 23 ^___3

27. y 1 __

5 x 6, (0, 3) 28. y 1 ^__4 x 2, (1, 0) m₁ 1 ^___m₂ 5

y 3 5( x 0) y 5x 3

m₁ 1 ^___m₂ 4 y 0 4( x 1) y 4x 4

(29)

1 Skills Practice

Name _____________________________________________ Date ____________________

Absolutely!

Absolute Value in Equations and Inequalities in One and

Two Variables

Vocabulary

Match each example with the term that describes it.

1. | x 2| 3 a. absolute value expression

b. absolute value equation

2. |3x| b. absolute value equation

a. absolute value expression

3. 2|3x 1| 2 5 c. absolute value inequality

c. absolute value inequality

4. 2  4x 5 8 d. compound inequality

d. compound inequality

Problem Set

Solve each equation.

5. |x 3| 4 6. |x 2| 5

x 3 4 x 2 5

x 7, 1 x 3, 7

7. |x 1| 2 7 8. |x 3| 4 10

|x 1| 5 | x 3| 14

x 1 5 x 3 14

x 4, 6 x 17, 11