**PARTICIPATION ACTIVITY**

2.3.1: Graphing a linear function: After plotting any two points, a line through those points represents all points of the function.

Start

2x speed

Lakewood Weddings

Fees:

$50 per person

y = 50x

x

y

40

2000

60

3000

10

20

30

40

50

60

70

1000

2000

3000

4000

0

0

70

3500

Shoreview Weddings

Fees:

$30 per person

y = 30x + 2000

x

y

40

3200

60

3800

10

20

30

40

50

60

70

1000

2000

3000

4000

0

2000

70

4100

$2000 setup

keyboard_arrow_downCaptions

**2.3.2: Identifying linear functions.**

Indicate whether the equation represents a linear function, which is an equation of two variables that can be written in the form y = mx + b, where m and b are constants.

1)

y = 2x + 50

Linear

Not linear

2)

y = 5x

Linear

Not linear

3)

y = 2x³ + 5

Linear

Not linear

4)

y = 8

Linear

Not linear

5)

y = 0.5x

Linear

Not linear

6)

y = (1/2)x

Linear

Not linear

7)

y = 2x + x + 1

Linear

Not linear

8)

y = 2 + 3x

Linear

Not linear

9)

A taxi fare is 3 dollars per ride, plus 2 dollars per mile driven (x). Is the equation for total fare (y) a linear function?

Yes

No

10)

The cost (y) of flooring for a square room can be written as an equation involving the length (x) of a side of the square room. Is the equation a linear function?

Yes

No

11)

A buffet restaurant charges 50 cents per year-of-age for a child. Is the price a linear function of a child’s age?

Yes

No

12)

A child starts with 15 dollars and spends 1 dollar per day. Is the amount of money left (y) a linear function of the number of days (x)?

Yes

No

**2.3.3: Graphing a linear equation to see the y value for a particular x value.**

Start

2x speed

Year

Savings ($)

1

2

3

4

5

6

7

8

9

10

2500

5000

7500

10000

12500

15000

y = 10000 + (10000 × 0.05 × x)

y = 10000 + 500x

Initial savings: $10000

$10500

$11000

After 10 years:

$15000

keyboard_arrow_downCaptions

**2.3.4: Savings y after x years.**

Consider the example above.

1)

Looking at the graph, what was the initial savings amount?

$

CheckShow answer

2)

Looking at the graph, what is the savings after 5 years?

$

CheckShow answer

3)

The graphs below show the savings assuming different interest rates: 4%, 5%, 6%, and 7%. After 10 years, how much more would be in savings for 7% compared to 4%? Use the graph to round each savings value to the nearest 500.

$

CheckShow answer

**2.3.5: Graphing linear equations helps compare those equations.**

Start

2x speed

Lakewood Weddings

10

20

30

40

50

60

70

1000

2000

3000

4000

y = 50x

80

90

100

5000

110

120

Shoreview Weddings

y = 30x + 2000

People

Cost (dollars)

Cost same

at 100 people

6000

7000

2500

keyboard_arrow_downCaptions

**2.3.6: Uses of linear function graphs.**

Answer the questions by just looking at the graphs above, without doing any calculations.

1)

What is the approximate cost for 75 people at Shoreview?

4000

5000

2)

Which venue is cheaper for 50 people?

Lakewood

Shoreview

3)

Shoreview has a large setup fee, but is cheaper per person. Shoreview is thus costlier for a small wedding. How many people must a wedding have before Shoreview becomes the cheaper venue overall?

50

100

4)

To see when the Lakewood cost equals the Shoreview cost, a person can write 50x = 30x + 2000.

Solving:

50x – 30x = 30x – 30x + 2000

20x = 2000

x = 100

To what graph parts does this calculation correspond?

Leftmost

Where the two graphs cross

Rightmost

**2.3.1: Linear functions.**

404272.1880072.qx3zqy7

Start

What are m and b in the linear equation y = 16x + 9?

m = b =

1

2

3

4

5

Check

Next

1

2

3

4

5

How many people must a wedding have before Shoreview becomes the cheaper venue overall?

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