2Linear Functions Linear means “line” Data is displayed as a LINE graph The general equation of a line is y=ax+b ORy=mx+b“a” or “m” is the slope OR RATE OF CHANGE“b” is the y-intercept OR STARTING POINTThe data trend is a STEADY increase or decrease
3EXAMPLES OF LINEAR FUNCTIONS FROM CLASS Earning hourly wage y=$8.00x+0where y=total pay earned$8.00 is the hourly rate of changex= number of hours workedb= starting pointWrite an linear function if the hourly wage is $9.25 per hour? y=_________________
4Linear Function for Minimum Wage Y= $9.50x or y=$9.50xwhere “x” is the number of hours worked
5EXAMPLES OF LINEAR FUNCTIONS FROM CLASS Profit, Loss, and BreakevenBe sure to include upfront costsUS Obesity RatesYearly Cost of Cell Phone PlansY=yearly cost of plan a=monthly rate x=# of months b=cost of phoneHeight and Foot Forensic ActivityPass the Tennis BallAlcohol Elimination RateUS Population Growth
6Graphing Linear Functions Using graph paper y=2x-1Make a table of x and y values to plot the pointsX ValuesY Values-1123
8Graphing Linear Functions using the Graphing Calculator Make LISTS. STAT. EDIT.Turn Plots On. 2nd y=.Set WINDOWGRAPH
9Finding 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.
10Bike 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.
11Bike Weights and Jump Heights Data TableGraphWeight in PoundsHeight in Inches1910.3519.510.32010.2520.510.22110.1229.8522.59.8239.7923.59.7249.6Is there a positive, negative, or no relationship between weight and jump height?
13Bike Weights and Jump Heights Find Linear Regression (or line of best fit)MeaningSTAT. 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=?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 _____
14Bike Weights and Jump Heights Y= (21.5) =Based on the linear regression, for each added pound of weight to the bike, the jump height decreases by-.156 inchAs the weight increases, the jump height __decreases__________
15Linear Functions and Cell Phone Plans November 28, 2013 WalMart AdWrite a Cell Phone Plan Linear FunctionUsing the WalMart Ad, write a linear function for that plan.Y=ax+by=total cost of phone plana= rate per month (slope or change)x= number of months in planb= cost of phone (starting point)Y=_________________________
16Linear Functions and Cell Phone Plans Write a Cell Phone Plan Linear FunctionUsing the WalMart Ad, write a linear function for that plan.Y=ax+by=total cost of phone plana= rate per month (slope or change)x= number of months in planb= cost of phone (starting point)Y= $45x + $299
17Quarterly Tests are 20% of Quarterly Math Grade You may use Review Sheet on TestBe 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!