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25 Cards in this Set

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APPLICATIONS OF LINEAR FUNCNTIONS-KEY WORDS
LINEAR FUNCTIONS
DIRECT VARIATIONS
GRAPHS
TABLES
LINE OF BEST FIT
INEQUALITIES SYSTEMS
SLOPES
INTERCEPTS
1ST OF THREE DISCRIPTOR HIGHLIGHTS-ONE
USE LINEAR FUNCTIONS IN MULTIPLE REPRESENTATIONS
2ND DISTRIBUTOR
USE THE PROPERTIES OF THE SLOPYE AND Y INTERCEPTS TO WORK WITH GRAPHS, TABLES, AND FUNCTIONS
THIRD DISTRIBUTOR
USE SYSTEMS OF LINEAR FUNCIONS AND EQUALITES
CHARACTERISTICS OF LINEAR FUNCTIONS
ALL VARIABLES HAVE A POWER OF 1
SLOPE: CONSTANT RATE OF CHANGE, RATE OF CHANGE IN Y OVER CHANGE IN X RATIO OF RISE OVER RUN-DESGINATIONS
M, _X2 -X1 /______B.
Y^2-y^1
SLOPE POSITIVE (M>), LINE STLANTS RIGHT
LINE SLANTS RIGHT
SLOPE IS NEGATIVE (M<0)
LINE SLANTS LEFT
ABSOLUTE VALUE OF A SLOPE: GREATER THAN 0 ((M} ) > 0
POINT IS (#, O))
ABSOLUTE VALYE OF SLOP: LESS THAN 0, ({M}<0) LINE IS MORE
HORIZONTAL
INTERCEPTS: WHERE THE GRAPH CROSSES THE X OR Y AXIS
X INTERCEOPT: Y-COORDIANTE IS ALWAYS 0 POINT IS (X, 0 ))
Y-INTERECEPT,: X-COORDINATE IS ALWAYS 0, POINT IS (0,Y)
LINEAR FUNCTION FORM
Y=MX+B, M IS THE SLOPE OF THE LINE 3/1 AN DY-INTERCEPT IS (0,5)
LINEAR FUNCTION FORM EAMPLE
Y=3X+5, SLOPE IS 3/1 AND Y-INTERCEEPT IS (0,5)
Y=MX + B
DEFINE POINT SLOPE: Y-YSUB1=M(X-XSUB1) M=SLOPE, (XSUB1, Y SUB 1) IS A SPECIFIC POINT
=SLOPE, (XSUB1, Y SUB 1) IS A SPECIFIC POINT
Y-3=2/3(X+2)...SLOPE=2/3, (-2, 3)
EXAMPLE : Y-3=2/3(X- -2)
STANDARD AX +BY=C -EXAMPLE
5X+4Y=20
REPREENTATIONS OF LINEAR FUNCTIONS-THIS SECTION WILL PRESENT A SITUATION AND SHOW YOU MULTIPLE REPRESENTATIONS OF LINEAR RELATIONSHIPS
LINER FUNCTIONS ARE USED TO MODEL SITUATIONS WHICH INVOLV A CONSTANT RATE OF CHANGE
LINEAR FUCTIONS CAN BE USED FOR THE FOLLOWING WHAT:
THEY CAN BE MODELED USING ***********CONCRETE MATERIALS, TABLE OF GRAPHS, AND FUNCTIONS EQUATIONS
REPRESENTATIONS OF LINEAR FUCNTION-REVIEW AND UNDERSTAND EXAMPLE 5 PAGE 59
DID YOU FINISH THE EXAMPLE 5, READ AND UNDERSTAND THOUOGHYLY?
porportional and direct variations
equal rations
example of proportional and direct variations-EXAMPLE
example: a scale model of a proposed building is constructed using the scale 2cm=1.8 m
FIND THE CONSTANT OF PROPORTIONALITY AND WRITE A SPECIFIC EQUATIONS EXPRESSING METERS IN TERMS OF CENTIMERTERS:
Y/X=1.8 M/2CM
2Y=1.8 X
Y=.9X-A CONSTANT PROPORTION OF .P
The CONSTANT OF PROPORTIONALITY IS .9
DIRECT VARIATION: A SPECIAL CASE OF A LINEAR FUNCTION WITH Y-INTERCEPT=0 EXAMPLE
THE NUMBER OF GALLONS OF GASOLINE USED DEPENDS ON THE NUMBER OF MILES TRAVELED. SUPPOSE A CAR USES 5 GALLOS OF GALLONS OF GASOLINE TO TRAVEL 120 MILES
CREATE A TABLE THAT WILL HELP YOU CREATE A FUNCTION FOR THIS SITUATIONS GALLONS=0, MILES, GALLONS= 5, MILES= 120),GALLONS 10, MILES 240)
SOLUTIONS TO LAST EXERCISE ON LAST CARD
SOLUTION: YOU KNOW THAT IF YOU DON'T TRAVEL YOU DON'T TRAVEL, OYOU DON'T USE THE GASOLINE. fROM THE TABLE IT IS EADY SEE THAT THE AVERAGE RATE OF USAGE IS 24 MILES/GAL. sINCE THIS IS A DIRECT VARIATION, THE FUNCTIONS IS M(G)=24 G OR MIES MILES=24(#GALLONS) 120/5
LINEAR FUNCTIONS TO MODEL DATA- THIS SIMPLY
MEANS TO LOOK FOR THE BEST LINE TO GO THROUGH THE DATA. iF YOU ARE LOOKING AT A GRAPH, FIND A RESONALBLE SLOPE AND Y-INTRCEPTS TO WRITE THE FUNCTION IF YOU ARE GIVEN A TAPLE, POLOT THE DATA AND FIND A REASONABLE SLOPE AND Y-INTERCEPT TO WRITE THE FUNCTIONS. YOU ARE GIVEN A TABLE, PLOT THE DAATA AND FIND A REASONABLE SLOPE AND Y-INTERCEPT TO WRITE THE FUNCTION. YOU ARE JUST USING THE SKILLS YOU ALREADY HAVE.
SYSTEMS OF LINEAR EQUATIONS AND INAEQUALITES
EQUATIONS: YOU HAVE Two EQUATIONS. IF YOU GRAPH THESE LINEAR EQUATIONS, THE POINT OF INTERSECTION IS A COMMON SOLUTION
DO EXAMPLES 1-3 IN TEXT MAKE SURE YOU UNDERSTAND ALL CONCEPTS
DO YOU UNDERSTAND THE EQUATION ANSWERS, CAN YOU DO THEM YOURSELF?