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
$2000 setup
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2.3.2: Identifying linear functions.
Indicate whether the equation represents a linear function, which is an equation of two variables that can be written in the form y = mx + b, where m and b are constants.
1)
y = 2x + 50
Linear
Not linear
2)
y = 5x
Linear
Not linear
3)
y = 2x³ + 5
Linear
Not linear
4)
y = 8
Linear
Not linear
5)
y = 0.5x
Linear
Not linear
6)
y = (1/2)x
Linear
Not linear
7)
y = 2x + x + 1
Linear
Not linear
8)
y = 2 + 3x
Linear
Not linear
9)
A taxi fare is 3 dollars per ride, plus 2 dollars per mile driven (x). Is the equation for total fare (y) a linear function?
Yes
No
10)
The cost (y) of flooring for a square room can be written as an equation involving the length (x) of a side of the square room. Is the equation a linear function?
Yes
No
11)
A buffet restaurant charges 50 cents per year-of-age for a child. Is the price a linear function of a child’s age?
Yes
No
12)
A child starts with 15 dollars and spends 1 dollar per day. Is the amount of money left (y) a linear function of the number of days (x)?
Yes
No
2.3.3: Graphing a linear equation to see the y value for a particular x value.
Start
2x speed
Year
Savings ($)
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
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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
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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.
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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
