1 What Makes a Function Linear Lesson 1.3

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.

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

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

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

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

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

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

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

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

11 Another Example Consider the following table of values  Note the value of for any two pairs of values C1 x C2 y

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

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

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?

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

16 Results Graph appears straight But … rate of change is not a constant tPslope

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