Linear Functions Wrap Up

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

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 pointWrite an linear function if the hourly wage is $9.25 per hour? y=_________________

Linear Function for Hourly Wage

Y= $9.25x + 0 or y=$9.25x where “x” is the number of hours worked

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

Graphing Linear Functions

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

X Values Y Values0 -11 12 3

Graphing Linear Functions

X Values Y Values0 -11 12 3

Graphing Linear Functions using the Graphing Calculator

• Make LISTS. STAT. EDIT.• Turn Plots On. 2nd y=.• Set WINDOW• GRAPH

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.

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.

Bike Weights and Jump Heights

Data TableWeight in Pounds Height in Inches

19 10.35

19.5 10.3

20 10.25

20.5 10.2

21 10.1

22 9.85

22.5 9.8

23 9.79

23.5 9.7

24 9.6

Graph• Is there a positive, negative, or no

relationship between weight and jump height?

Bike Weights and Jump Heights

Bike Weights and Jump Heights

Find Linear Regression (or line of best fit)

• 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=?

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 _____

Bike Weights and Jump Heights

Y= -.156(21.5)+13.358=

As the weight increases, the jump height __decreases__________

Based on the linear regression, for each added pound of weight to the bike, the jump height decreases by -.156 inch

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=_________________________

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

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!