1. SECTION 2.2 BUILDING LINEAR FUNCTIONS FROM DATA BUILDING LINEAR FUNCTIONS FROM DATA

2. LINEAR CURVE FITTING STEP 1: Ask whether the variables are related to each other. STEP 1: Ask whether the variables are related to each other. STEP 2: Obtain data and verify a relation exists. Plot the points to obtain a scatter diagram. STEP 2: Obtain data and verify a relation exists. Plot the points to obtain a scatter diagram. STEP 3: Find an equation which describes this relation. STEP 3: Find an equation which describes this relation.

3. FINDING AN EQUATION FOR LINEARLY RELATED DATA A farmer collected the following data, which shows crop yields for various amounts of fertilizer used. A farmer collected the following data, which shows crop yields for various amounts of fertilizer used.

4. Fertilizer (X lbs)Yield (Y bushels) 04 06 510 57 1012 1010 1515 1517 2018 2021 2523 2522

5. GETTING A SCATTER PLOT OF THE DATA Ensure that all equations in the Y= menu are cleared out or disabled. Input the data into the lists in the statistics editor: STAT 1:Edit Turn on a Statistics Plotter and set the desired parameters: 2nd Y= Push Zoom and choose ZoomStat.

6. GETTING A LINE OF BEST FIT Verify by the scatter plot that the data has a linear relationship. Go to the home screen, press STAT, arrow to CALC, and choose LinReg. A linear regression equation will appear in the home screen.

7. GRAPHING THE REGRESSION EQUATION To put the regression equation in the Y= menu: 1. Push Y= 2. Push VARS, choose Statistics, arrow to EQ, and choose RegEQ. Now push GRAPH.

8. MAKING A PREDICTION Use the Linear Regression Equation to Estimate the Yield if the farmer uses 17 pounds of fertilizer. 1. Go to home screen 2. Go into YVARS, choose Function, Choose Y 1. 3.Type in (17).

9. MAKING A PREDICTION Our prediction is that the crop yield for 17 Pounds of fertilizer per 100 ft 2 will be 17 Bushels

10. CONCLUSION OF SECTION 2.2 CONCLUSION OF SECTION 2.2

11. VARIATION Relationships between variables are often described in terms of proportionality. For Example: Force is proportional to acceleration. Pressure and volume of an ideal gas are inversely proportional.

12. DIRECT VARIATION Let x and y denote two quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number k such that y = kx constant of proportionality

13. EXAMPLE For a certain gas enclosed in a container of fixed volume, the pressure P (in newtons per square meter) varies directly with temperature T (in kelvins). If the pressure is found to be 20 newtons/m 2 at a temperature of 60 K, find a formula that relates pressure P to temperature T. Then find the pressure P when T = 120 K.

14. SOLUTION First, we know that P varies directly with T. P = k T And, we know P = 20 when T = 60. Thus, 20 = k(60)

15. SOLUTION The formula, then, is Now, we must find P when T = 120K P = 40 newtons per square meter