5-1 Identifying Linear Functions - Home - Manchester Local … · 2016-02-11 · 5-44 Holt McDougal...

Name ________________________________________ Date __________________ Class__________________

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5-3 Holt McDougal Algebra 1

Practice A Identifying Linear Functions

Use the graph for 1–3. 1. Is this graph a function? _______________

2. Explain how you know it is a function.

____________________________________________________

____________________________________________________

3. If this graph is a function, is it also a linear function? _______________

Use the set {(1, 8), (2, 6), (3, 4), (4, 2), (5, 0)} for 4–5.

4. Does the set of ordered pairs satisfy a linear function? ___________________________ 5. Explain how you decided. __________________________________________________________

_________________________________________________________________________________________

6. Write the equation y = x − 4 in standard form (Ax + By = C).

_________________________________________

7. Is y = x − 4 a linear function?

_________________________________________

8. Graph y = x − 4 to check. 9. In 2005, a storm in Milwaukee, WI was dropping 2.5

inches of snow every hour. The total amount of snow is given by f(x) = 2.5x, where x is the number of hours. Graph this function and give its domain and range.

_________________________________________

LESSON

5-1

Name ________________________________________ Date __________________ Class__________________



Practice B Identifying Linear Functions

Identify whether each graph represents a function. Explain. If the graph does represent a function, is the function linear?

1. ___________________________________________________________

___________________________________________________________

___________________________________________________________

2. ___________________________________________________________

___________________________________________________________

___________________________________________________________ 3. Which set of ordered pairs satisfies a linear function? Explain. Set A: {(5, 1), (4, 4), (3, 9), (2, 16), (1, 25)} _________________________________________

Set B: {(1, −5), (2, −3), (3, −1), (4, 1), (5, 3)} _________________________________________

4. Write y = −2x in standard form. Then graph the function.

______________________________________________________

5. In 2005, the Shabelle River in Somalia rose an estimated 5.25 inches every hour for 15 hours. The increase in water level is represented by the function f(x) = 5.25x, where x is the number of hours. Graph this function and give its domain and range.

______________________________________________________

LESSON

5-1

Name ________________________________________ Date __________________ Class__________________



Practice A Using Intercepts

Find the x- and y-intercepts. 1.

2. 3.

x-intercept: _____________ x-intercept: _____________ x-intercept: _____________ y-intercept: _____________ y-intercept: _____________ y-intercept: _____________ 4. Find the intercepts of 2x + 3y = 6 by following the steps below.

a. Substitute y = 0 into the equation. Solve for x.

_______________________________________________

b. The x-intercept is: ________________________ c. Substitute x = 0 into the equation. Solve for y.

_______________________________________________

d. The y-intercept is: ________________________ e. Use the intercepts to graph the line described by the equation.

5. Jennifer started with $50 in her savings account. Each week she withdrew $10. The amount of money in her savings account after x weeks is represented by the function f(x) = 50 − 10x. a. Find the intercepts and graph the function.

_______________________________________________

b. What does each intercept represent?

_______________________________________________

_______________________________________________

_______________________________________________

LESSON

5-2

Name ________________________________________ Date __________________ Class__________________



Practice B Using Intercepts

Find the x- and y-intercepts. 1.

2.

3.

________________________ _________________________ ________________________

________________________ ________________________ ________________________

Use intercepts to graph the line described by each equation.

4. 3x + 2y = −6 5. x − 4y = 4

6. At a fair, hamburgers sell for $3.00 each and hot dogs sell for

$1.50 each. The equation 3x + 1.5y = 30 describes the number of hamburgers and hot dogs a family can buy with $30. a. Find the intercepts and graph the function.

_______________________________________________

b. What does each intercept represent?

_______________________________________________

_______________________________________________

_______________________________________________

_______________________________________________

LESSON

5-2

Name ________________________________________ Date __________________ Class__________________



Practice A Rate of Change and Slope

Fill in the blanks to define slope. 1. The ___________ is the difference in the y-values of two points on a line. 2. The ___________ is the difference in the x-values of two points on a line. 3. The slope of a line is the ratio of ___________ to ___________ for any two points on the line.

Find the rise and run between each set of points. Then, write the slope of the line. 4.

5.

6.

slope = _______________ slope = _______________ slope = _______________

Tell whether the slope of each line is positive, negative, zero, or undefined. 7.

8.

9.

________________________ _________________________ ________________________

10. The table shows a truck driver’s distance from home during one day’s deliveries. Find the rate of change for each time interval.

Time (h) 0 1 4 5 8 10

Distance (mi) 0 35 71 82 199 200

Hour 0 to Hour 1: _________ Hour 1 to Hour 4: _________ Hour 4 to Hour 5: _________

Hour 5 to Hour 8: _________ Hour 8 to Hour 10: _________

The rate of change represents the average speed. During which time interval was the driver’s average speed the least? _________________________________

LESSON

5-3

Name ________________________________________ Date __________________ Class__________________



Practice B Rate of Change and Slope

Find the rise and run between each set of points. Then, write the slope of the line.

1.

2.

3.

rise = ______ run = ______ rise = ______ run = ______ rise = ______ run = ______


4.

5.

6.

rise = ______ run = ______ rise = ______ run = ______ rise = ______ run = ______


Tell whether the slope of each line is positive, negative, zero, or undefined. 7.

8.

9.

________________________ _________________________ ________________________

10. The table shows the amount of water in a pitcher at different times. Graph the data and show the rates of change. Between which two hours is the rate of change the greatest? _______________

Time (h) 0 1 2 3 4 5 6 7

Amount (oz) 60 50 25 80 65 65 65 50

LESSON

5-3

Name ________________________________________ Date __________________ Class__________________



Practice A The Slope Formula

Find the slope of the line that contains each pair of points. 1. (3, 1) and (9, 2) 2. (−2, 3) and (2, −1) 3. (4, 6) and (0, −2)

m = 2 1

2 1

y yx x

−−

m = 2 1

2 1

y yx x

−−

m = 2 1

2 1

y yx x

−−

= 2 1

−−

= 1

= 1 2 − −−

=

= =

−−

=

=

Each graph or table shows a linear relationship. Find the slope. 4. 5. 6.

________________________ _________________________ ________________________

Find the slope of each line. Then tell what the slope represents. 7. 8.

_________________________________________ ________________________________________

_________________________________________ ________________________________________

Complete the steps to find the slope of the line described by 2x + 5y = 10. 9. a. Find the x-intercept. b. Find the y-intercept. c. The line contains (____, 0) Let y = 0 Let x = 0 and (0, _____). Use the 2x + 5 (_____) = −10 2 (_____) + 5y = −10 slope formula.

_______ = −10 _______ = −10

÷ _______ ÷ _______ ÷ _______ ÷ _______

x = ________ y = ________

LESSON

5-4

x y

0 82

3 76

6 70

9 64

12 58

m = 2 1

2 1

y yx x

−−

= 00

−−

=

Name ________________________________________ Date __________________ Class__________________



Practice B The Slope Formula

Find the slope of the line that contains each pair of points. 1. (2, 8) and (1, −3) 2. (−4, 0) and (−6, −2) 3. (0, −2) and (4, −7)

m = 2 1

2 1

y yx x

−−

m = 2 1

2 1

y yx x

−−

m = 2 1

2 1

y yx x

−−

=

−−

=

−−

=

−−

=

= =

= =

Each graph or table shows a linear relationship. Find the slope. 4. 5. 6.

________________________ _________________________ ________________________

Find the slope of each line. Then tell what the slope represents. 7. 8.

_________________________________________ ________________________________________

_________________________________________ ________________________________________

Find the slope of the line described by each equation. 9. 3x + 4y = 24 10. 8x + 48 = 3y

_________________________________________ ________________________________________

LESSON

5-4

x y

1 3.75

2 5

3 6.25

4 7.50

5 8.75

Name ________________________________________ Date __________________ Class__________________



Practice A Direct Variation

Complete the table.

Solve for y (if needed).

Is the equation in the form y = kx?

Is it a direct variation?

Constant of variation

1. y = 7x y = 7x yes yes

2. y = 4x − 10

3. 5x − 2y = 0

Complete the table.

Find the value of yx

for each ordered pair.

Is the value of yx

the same

for each ordered pair?

Direct variation?

4.

5.

6. The value of y varies directly with x, and y = −2 when x = −4. Find y when x = 8.

Find k: Use k to find y: y = kx y = kx −2 = k(−4) y =

_____( ) _____( )

______ = k y = __________

7. The value of y varies directly with x, and y = 12 when x = 8. Find y when x = 15.

Find k: Use k to find y: y = kx y = kx 12 = k(8) y =

_____( ) _____( )

_____ = k y = __________ 8. The number of hamburgers that can be

made varies directly with the weight of ground beef used. Four hamburgers can be produced from every pound of ground beef. Write a direct variation equation for the number of hamburgers y that can be produced from x pounds of ground beef. Then graph the relationship.

_________________________________________

LESSON

5-5

x 4 8 12 y 16 20 24

x 10 15 20 y 2 3 4

Name ________________________________________ Date __________________ Class__________________



Practice B Direct Variation

Tell whether each equation is a direct variation. If so, identify the constant of variation. 1. y = 3x _________________ 2. y = 2x − 9 _________________ 3. 2x + 3y = 0 _________________ 4. 3y = 9x _________________

Find the value of yx for each ordered pair. Then, tell whether each

relationship is a direct variation.

5. x 6 15 21

y 2 5 7

yx

6. x 6 10 25

y 24 40 100

yx

7. x 10 15 20

y 3 5 9

yx

________________________ _________________________ ________________________

8. The value of y varies directly with x, and y = −18 when x = 6. Find y when x = −8.

Find k: Use k to find y:

y = kx

y = _____( ) _____( )

_____ = k y = __________

9. The value of y varies directly with x,

and y = 12

when x = 5.

Find y when x = 30.

Find k: Use k to find y:

y = kx

y = _____( ) _____( )

_____ = k y = __________ 10. The amount of interest earned in a savings account

varies directly with the amount of money in the account. A certain bank offers a 2% savings rate. Write a direct variation equation for the amount of interest y earned on a balance of x. Then graph.

_________________________________________

11. Another bank offers a different savings rate. If an account with $400 earns interest of $6, how much interest is earned by an account with $1800?

_________________________________________

LESSON

5-5

Name ________________________________________ Date __________________ Class__________________



Practice A Slope-Intercept Form

Write the equation that describes each line in slope-intercept form.

1. slope = 23

; y-intercept = 2

y = ______ x + ______ 2. slope = −1; y-intercept = −8 y = ______ x − ______

3. slope = −2; (3, 5) is on the line. Find the y-intercept: y = mx + b

5 = (−2)(___) + b5 = ___+ b

+ ____+ ________ = b

Write the equation: y = ______ x + ______

Write each equation in slope-intercept form. Then graph the line.

4. y − 2x = −4 5. y − 3 = − 12

x 6. 2x + 3y = 6

________________________ _________________________ ________________________

7. A school orders 25 desks for each classroom,

plus 30 spare desks. The total number ordered as a function of the number of classrooms is shown in the graph. a. Write the equation represented by the graph.

_____________________________________

b. Identify the slope and y-intercept and describe their meanings. ________________________________________

____________________________________________________

c. Find the total number of desks ordered if there are 24 classrooms.

___________________________________________________

LESSON

5-6

Name ________________________________________ Date __________________ Class__________________



Practice B Slope-Intercept Form

Write the equation that describes each line in slope-intercept form. 1. slope = 4; y-intercept = −3 y = _______________________ 2. slope = −2; y-intercept = 0 y = _______________________

3. slope = − 1

3; y-intercept = 6

y = _______________________

4. slope = 25

, (10, 3) is on the line.

Find the y-intercept y = mx + b

____ = (____)____ + b

____ = ____ + b

____ = b

Write the equation: y = ______________

Write each equation in slope-intercept form. Then graph the line described by the equation.

5. y + x = 3 6. y + 4 = 43

x 7. 5x − 2y = 10

________________________ _________________________ ________________________

8. Daniel works as a volunteer in a homeless shelter.

So far, he has worked 22 hours, and he plans to continue working 3 hours per week. His hours worked as a function of time is shown in the graph.

a. Write an equation that represents the hours Daniel will work as a function of time. _____________________ b. Identify the slope and y-intercept and describe their meanings. ________________________________________

___________________________________________________

c. Find the number of hours worked after 16 weeks.

___________________________________________________

LESSON

5-6

Name ________________________________________ Date __________________ Class__________________



Practice A Point-Slope Form

Match each graph with the correct slope and point.

1. slope = 12 ; (0, 2) ______ 2. slope = −

12 ; (2, 0) ______ 3. slope = −2; (2, 0) ______

A B C

Write an equation in point-slope form for the line with the given slope that contains the given point.

4. slope = 4; (3, 8) 5. slope = −12 ; (5, −3)

_________________________________________ ________________________________________

Write the equation that describes each line in slope-intercept form. 6. slope = 5; (1, 7) is on the line 7. slope = −3; (4, 0) is on the line

_________________________________________ ________________________________________

8. (0, 2) and (2, 6) are on the line 9. (8, −2) and (4, −4) are on the line

_________________________________________ ________________________________________

Find the intercepts of the line that contains each pair of points. 10. (2, 5) and (−6, 25) __________________ 11. (2, 9) and (−4, −9) __________________

12. The cost to have T-shirts made with the school logo is a function

of the number of T-shirts ordered. The costs for 20, 50, and 100 shirts are shown. Write an equation in slope-intercept form that represents the function. Then find the cost of ordering 130 T-shirts.

_________________________________________

LESSON

5-7

T-shirts 20 50 100Cost ($) 190 430 830

Name ________________________________________ Date __________________ Class__________________



Practice B Point-Slope Form

Write an equation in point-slope form for the line with the given slope that contains the given point. 1. slope = 3; (−4, 2) 2. slope = −1; (6, −1)

_________________________________________ ________________________________________

Graph the line described by each equation.

3. y + 2 = − 2

3 (x − 6) 4. y + 3 = − 2 (x − 4)

Write the equation that describes the line in slope-intercept form.

5. slope = −4; (1, −3) is on the line 6. slope = 12

; (−8, −5) is on the line

_________________________________________ ________________________________________

7. (2, 1) and (0, −7) are on the line 8. (−6, −6) and (2, −2) are on the line

_________________________________________ ________________________________________

Find the intercepts of the line that contains each pair of points. 9. (−1, −4) and (6, 10) __________________ 10. (3, 4) and (−6, 16) __________________

11. The cost of internet access at a cafe is a function of time. The costs for 8, 25, and 40 minutes are shown. Write an equation in slope-intercept form that represents the function. Then find the cost of surfing the web at the cafe for one hour.

_________________________________________

LESSON

5-7

Time (min) 8 25 40 Cost ($) 4.36 7.25 9.80

Name ________________________________________ Date __________________ Class__________________



Practice A Slopes of Parallel and Perpendicular Lines

Circle the equations whose lines are parallel.

1. y = 4; y = 12

x + 3; y = 12

x; y = 2x

2. y − 5 = 6(x + 2); y = −6x; 6x + y = 4; y = 6 3. Find the slope of each segment.

slope of AB : ____________________________

slope of AD : ____________________________

slope of DC : ____________________________

slope of BC : ____________________________ Explain why ABCD is a parallelogram.

_________________________________________________________________________________________

_________________________________________________________________________________________

Circle the equations whose lines are perpendicular. 4. y = x − 4; y = 3; y = −x; y = −3

5. y = 5x + 1; y = 3; y = 15

x; x = 5

6. y = 13

x − 2; x = 2; y − 4 = 3(x + 3); y = −3x + 9

7. Find the slope of each segment.

slope of AB : ______________________________

slope of BC : _____________________________

slope of AC : ____________________________

Explain why ABC is a right triangle.

_________________________________________________________________________________________

_________________________________________________________________________________________

LESSON

5-8

Name _______________________________________ Date __________________ Class__________________



Practice B

Slopes of Parallel and Perpendicular Lines

Identify which lines are parallel.

1. y = 3x + 4; y = 4; y = 3x; y = 3

________________________________________________________________________________________

2. y =

1

2x + 4; x =

1

2; 2x + y = 1; y =

1

2x + 1

________________________________________________________________________________________

3. Find the slope of each segment.

slope of AB : ____________________________

slope of AD : ____________________________

slope of DC : ____________________________

slope of BC : ____________________________

Explain why ABCD is a parallelogram.

________________________________________________________________________________________

________________________________________________________________________________________

Identify which lines are perpendicular.

4. y = 5; y =

1

8x; x = 2; y = 8x 5

________________________________________________________________________________________

5. y = 2; y =

1

2x 4; y 4 = 2(x + 3); y = 2x

________________________________________________________________________________________

6. Show that ABC is a right triangle.

_______________________________________

_______________________________________

_______________________________________

_______________________________________

_______________________________________

LESSON

5-8

Name ________________________________________ Date __________________ Class__________________



Practice A Transforming Linear Functions

Fill in each blank with translation, rotation, or reflection. 1. A __________________________________ is like a turn. 2. A __________________________________ is like a slide. 3. A __________________________________ is like a flip.

Graph f(x) and g(x). Then describe the transformation(s) from the graph of f(x) to the graph of g(x). 4. f(x) = x; g(x) = x + 5

__________________________________________

__________________________________________

__________________________________________

5. f(x) = 2x − 1; g(x) = 4x − 1

__________________________________________

__________________________________________

__________________________________________

6. f(x) = x; g(x) = 12

x − 7

__________________________________________

__________________________________________

__________________________________________

7. The cost of making a ceramic picture frame at a paint-your-own pottery store is $12, plus $5 per hour while you paint. The total cost for the frame that you spend x hours painting is f(x) = 5x + 12. a. How will the graph of this function change if the cost of the frame is raised to $15?

_____________________________________________________________________________________

b. How will the graph of this function change if the hourly charge is lowered to $4?

_____________________________________________________________________________________

LESSON

5-9

Name ________________________________________ Date __________________ Class__________________



Practice B Transforming Linear Functions

Graph f(x) and g(x). Then describe the transformation from the graph of f(x) to the graph of g(x). 1. f(x) = x; g(x) = x + 3

__________________________________________

__________________________________________

__________________________________________

2. f(x) = 13

x − 4; g(x) = 14

x − 4

__________________________________________

__________________________________________

__________________________________________

3. f(x) = x; g(x) = 2x − 5

__________________________________________

__________________________________________

__________________________________________

4. Graph f(x) = −3x + 1. Then reflect the graph of f(x) across the y-axis. Write a function g(x) to describe the new graph.

__________________________________________

5. The cost of hosting a party at a horse farm is a flat fee of $250, plus $5 per person. The total charge for a party of x people is f(x) = 5x + 250. How will the graph of this function change if the flat fee is lowered to $200? if the per-person rate is raised to $8?

_________________________________________________________

_________________________________________________________

_________________________________________________________

LESSON

5-9

5-1 Identifying Linear Functions - Home - Manchester Local … · 2016-02-11 · 5-44 Holt McDougal...

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