1 What Makes a Function Linear Lesson 1.3. 2 What Is A Line? Check out this list of definitions or...
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Transcript of 1 What Makes a Function Linear Lesson 1.3. 2 What Is A Line? Check out this list of definitions or...
2
What Is A Line?
Check out this list of definitions or explanations to the questionDefine Line
Today we look at what makes a function linear.
3
Rate of Change
Consider example y = 3x + 5We note the rate of change is constantThis means it is a linear function It graphs as a straight line
y=3x + 5
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Plotting Points on the Calculator
Use Data Matrix on Calculator
Choose APPS, then 6 Data/Matrixthen NEW
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Entering Data
Enter numeric values in the cells Enter a formula at the top
Using column nameCursor must be here
Enter formula here
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Viewing Data
Note the results of the formula We can do further calculations We can also plot these points
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Plotting Data
Choose F2 for Plot SetupScreen
Then F1 for Define
Choose line type
Specify the columns for the X and Y values
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Plotting Data
Goto the Y= Screen to turn off any functions there
Then specify ZoomDataThis fits the window to the limits of the data
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Plotting Data
Note the graph includes the points we had in the data matrix
It is a line-graph, the points are represented by boxes
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Another Example
Consider the following table of values Note the value of
for any two pairs of values
C1x
C2y
3 6
4 9
5 12
6 15
y
x
2x 6y 3x 9y 3
y
x
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Example From Text
See Example 2, pg. 19 Formula used for depreciation
Value of equipment = original value – $4000 * number of years
To generalize:
Dependent Qty = startValue + rateOfChange * independentQuantity
y m x b
$20,000
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Family of Linear Functions
Slope = Rate of Change
change in y
change in x
constant rate of change
y m x b
ym slope
x
y=3x + 5• Slope = m = 3
• y-intercept = b = 5
View TI Nspire filewhich demonstrates
the slope-intercept formula
View TI Nspire filewhich demonstrates
the slope-intercept formula
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Family of Linear Functions
Calculating slope with two ordered pairs
•
•(X1, Y1)
(X2, Y2)
xy
1 2
1 2
y yslope
x x
Given two ordered pairs, (7,5) and (-3,12). What is the slope of the line
through these two points?
5 12 70.7
7 ( 3) 10
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Warning
Not all functions which appear linear will actually be linear!!
Consider the set of ordered pairsGraph themDecide whether graph
is linearCheck slope for different
pairs
t P
0 67.38
1 69.13
2 70.93
3 72.77
4 74.67
5 76.61
6 78.60
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Results
Graph appearsstraight
But …rate of change is not a constant
66
68
70
72
74
76
78
80
0 2 4 6 8
t P slope
0 67.38
1 69.13 1.75
2 70.93 1.8
3 72.77 1.84
4 74.67 1.9
5 76.61 1.94
6 78.6 1.99