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1 What Makes a Function Linear Lesson 1.3

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2 What Is A Line? Check out this list of definitions or explanations to the question Define Line Define Line Today we look at what makes a function linear.

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3 Rate of Change Consider example y = 3x + 5 We note the rate of change is constant This means it is a linear function It graphs as a straight line y=3x + 5

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4 Plotting Points on the Calculator Use Data Matrix on Calculator Choose APPS, then 6 Data/Matrix then NEW

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5 Starting Up Choose DATA Give it a variable name for saving in memory

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6 Entering Data Enter numeric values in the cells Enter a formula at the top Using column name Cursor must be hereEnter formula here

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7 Viewing Data Note the results of the formula We can do further calculations We can also plot these points

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8 Plotting Data Choose F2 for Plot Setup Screen Then F1 for Define Choose line type Specify the columns for the X and Y values

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9 Plotting Data Goto the Y= Screen to turn off any functions there Then specify ZoomData This fits the window to the limits of the data

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10 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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11 Another Example Consider the following table of values Note the value of for any two pairs of values C1 x C2 y 36 49 512 615

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12 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 $20,000

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13 Family of Linear Functions Slope = Rate of Change y=3x + 5 Slope = m = 3 y-intercept = b = 5 View TI Nspire filewhich demonstrates the slope-intercept formula

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14 Family of Linear Functions Calculating slope with two ordered pairs (X 1, Y 1 ) (X 2, Y 2 ) Given two ordered pairs, (7,5) and (-3,12). What is the slope of the line through these two points?

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15 Warning Not all functions which appear linear will actually be linear!! Consider the set of ordered pairs Graph them Decide whether graph is linear Check slope for different pairs tP 067.38 169.13 270.93 372.77 474.67 576.61 678.60

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16 Results Graph appears straight But … rate of change is not a constant tPslope 067.38 169.131.75 270.931.8 372.771.84 474.671.9 576.611.94 678.61.99

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17 Assignment Lesson 1.3 Page 24 Exercises 1 – 5, 7, 9, 13, 15, 19, 21, 23

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