Linear Functions Wrap Up

1. Linear Functions Wrap Up

2. Linear Functions • Linear means “line” • Data is displayed as a LINE graph • The general equation of a line is y=ax+b OR y=mx+b • “a” or “m” is the slope OR RATE OF CHANGE • “b” is the y-intercept OR STARTING POINT • The data trend is a STEADY increase or decrease

3. EXAMPLES OF LINEAR FUNCTIONS FROM CLASS • Earning hourly wage y=$8.00x+0 where y=total pay earned $8.00 is the hourly rate of change x= number of hours worked b= starting point Write an linear function if the hourly wage is $9.25 per hour? y=_________________

4. Linear Function for Minimum Wage Y= $9.50x + 0 or y=$9.50x where “x” is the number of hours worked

5. EXAMPLES OF LINEAR FUNCTIONS FROM CLASS • Profit, Loss, and Breakeven • Be sure to include upfront costs • US Obesity Rates • Yearly Cost of Cell Phone Plans • Y=yearly cost of plan a=monthly rate x=# of months b=cost of phone • Height and Foot Forensic Activity • Pass the Tennis Ball • Alcohol Elimination Rate • US Population Growth

6. Graphing Linear Functions • Using graph paper y=2x-1 • Make a table of x and y values to plot the points

7. Graphing Linear Functions

8. Graphing Linear Functions using the Graphing Calculator • Make LISTS. STAT. EDIT. • Turn Plots On. 2nd y=. • Set WINDOW • GRAPH

9. Finding Line of Best Fit or Linear Regression for Data using Graphing Calculator • Enter data in LISTS. STAT. EDIT. • STAT. CALC. #4 LinReg (ax+b),L1,L2,VARS,Y-VARS, Enter, Enter, Enter. • Line of Best Fit should appear in y=. • 2nd WINDOW for TABLESET. • 2nd GRAPH for TABLE.

10. Bike Weights and Jump Heights • In BMX dirt-bike racing, jumping high or “getting air” depends on many factors: the rider’s skill, the angle of the jump, and the weight of the bike. The table below displays data that relate bike weight to maximum height. The activity which follows uses this data to determine a line of best fit to better predict the height from the weight of the bike.

11. Bike Weights and Jump Heights Data Table Graph Is there a positive, negative, or no relationship between weight and jump height?

12. Bike Weights and Jump Heights

13. Bike Weights and Jump Heights Find Linear Regression (or line of best fit) Meaning As the weight increases, the jump height ____________ Based on the linear regression, for each added pound of weight to the bike, the jump height decreases by _____ • STAT. CALC. #4 LinReg (ax+b) L1, L2, VARS, Y-VARS. #1 Function. #1 Y1. ENTER. • y= _________________ • Look at TABLE. Predict what the maximum jump height would be if bike weight is 21.5 lbs. If x=21.5, y=?

14. Bike Weights and Jump Heights Y= -.156(21.5)+13.358= Based on the linear regression, for each added pound of weight to the bike, the jump height decreases by -.156 inch As the weight increases, the jump height __decreases__________

15. Linear Functions and Cell Phone Plans November 28, 2013 WalMart Ad Write a Cell Phone Plan Linear Function Using the WalMart Ad, write a linear function for that plan. Y=ax+b y=total cost of phone plan a= rate per month (slope or change) x= number of months in plan b= cost of phone (starting point) Y=_________________________

16. Linear Functions and Cell Phone Plans • Write a Cell Phone Plan Linear Function • Using the WalMart Ad, write a linear function for that plan. • Y=ax+b • y=total cost of phone plan • a= rate per month (slope or change) • x= number of months in plan • b= cost of phone (starting point) • Y= $45x + $299

17. Quarterly Tests are 20% of Quarterly Math Grade • You may use Review Sheet on Test • Be sure to complete and turn in ALL missing work prior to close of quarter. Homework assignments are 20% of Quarterly Math Grade. • As always, do your best!