LESSON Reteach Graphing Linear Functions

1 Copyright by Holt, Rinehart and Winston. 22 Holt Algebra 2 All rights intercepts to sketch the graph of the function 3x 6y x-intercept is where the graph crosses the x-axis. To find the x-intercept, set y 0 and solve for x. 3x 6y 12 3x 6(0) 12 3x 12x 4 The y-intercept is where the graph crosses the y-axis. To find the y-intercept, set x 0 and solve for y. 3x 6y 12 3(0) 6y 12 6y 12y 2 Plot the points ( 4, 0) and ( 0, 2). Draw a line connecting the the intercepts and graph each Date ClassReteachGraphing Linear Functions2-3 LESSON 1. 3x 2y 6 a. 3x 2 6 x-intercept b. 3 2y 6 y-intercept 2. 6x 3y 12 a. 6x 3 12 x-intercept b. 6 3y 12 y-intercept The y-intercept occurs at the point 0, 2 .The x-intercept occurs at the point 4, 0.

2 2 x x 2212/7/05 6:28:36 PMCopyright by Holt, Rinehart and Winston. 23 Holt Algebra 2 All rights each function in slope-intercept form. Use m and b to Linear Functions (continued)Name Date Class2-3 LESSONy mx b is the slope-intercept represents the slope and b represents the the slope and the y-intercept to graph a Linear write 2y x 6 in slope-intercept form, solve for y. 2y x 6 x x 2y x 6 2y ___ 2 x __ 2 6 __ 2 y 1 __ 2 x 3 Compare y 1 __ 2 x 3 to y mx 1 __ 2 , so the slope is 1 __ 2 .b 3, so the y-intercept is 3. 3. 2x y 1a. y x b. m c. b x __ 2 1a. y b. m c. b 2 x x 2312/7/05 6:28:37 PMCopyright by Holt, Rinehart and Winston.

3 79 Holt Algebra 2 all rights reserved .#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/. * >V Vi 'RAPHING ,INEAR &UNCTIONS$ETERMINE IF THE RATE OF CHANGE CHANGE IN F S X D ?????????????? CHANGE IN X IS CONSTANT 4 HEN TELL WHETHER EACH DATA SET REPRESENTS A Linear OR NONLINEAR FUNCTION X F S X D X F S X D Linear NONLINEAR0 LOT THE GIVEN POINT 5SE THE SLOPE TO FIND A SECOND POINT 4 HEN GRAPH THE LINE POINT S D SLOPE POINT S D SLOPE ??? XY XY )DENTIFY THE X INTERCEPT AND THE Y INTERCEPT FOR EACH LINE X Y X Y X Y Y X Y X Y X X Y X Y X Y ??? 7 RITE EACH FUNCTION IN SLOPE INTERCEPT FORM Y MX B X Y Y X X Y X Y X X Y X Y X Y X ??? ?? #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/. * >V Vi 'RAPHING ,INEAR &UNCTIONS$ETERMINE WHETHER EACH DATA SET COULD REPRESENT A Linear FUNCTION X F S X D X F S X D.)))

4 ONLINEAR ,INEAR5SE THE COORDINATE PLANE AT RIGHT TO GRAPH AND LABEL EACH LINE ,INE A HAS A SLOPE OF AND PASSES THROUGH S D ,INE B HAS A SLOPE OF AND PASSES THROUGH S D ,INE C HAS A SLOPE OF ?? AND PASSES THROUGH S D ,INE D HAS A SLOPE OF ??? AND PASSES THROUGH S D &IND THE INTERCEPTS OF EACH LINE AND GRAPH AND LABEL THE LINE LINE E X Y X INTERCEPT Y INTERCEPT LINE F X Y X INTERCEPT Y INTERCEPT 7 RITE EACH FUNCTION IN SLOPE INTERCEPT FORM 4 HEN GRAPH AND LABEL THE FUNCTION LINE G X Y Y X LINE H X Y Y X ???? $ETERMINE WHETHER EACH LINE IS VERTICAL OR HORIZONTAL X Y ?? X 6 ERTICAL (ORIZONTAL 6 ERTICALACBDXY HFGEXY #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/.* >V Vi 'RAPHING ,INEAR &UNCTIONS %VERY TIME )MANI BUYS GAS FOR HER CAR SHE RECORDS THE NUMBER OF GALLONS REQUIRED TO FILL THE TANK AND THE NUMBER OF MILES SHE HAS DRIVEN SINCE THE LAST FILL UP A $OES THE DATA SET REPRESENT A Linear FUNCTION %XPLAIN HOW YOU KNOW.))

5 O THE DATA SET IS NONLINEAR 0 OSSIBLE ANSWER 4HE DIFFERENCE BETWEEN THE DATA ITEMS IS NOT CONSISTENT OR PROPORTIONAL B 7 HAT DOES IT MEAN IN TERMS OF THE WAY A CAR USES GAS FOR THE DATA TO BE Linear OR NONLINEAR 0 OSSIBLE ANSWER )T IS APPROPRIATE FOR THE DATA TO BE NONLINEAR SINCE A CAR USES GAS DIFFERENTLY DEPENDING ON WHERE AND HOW IT IS BEING DRIVEN *ULIAN READ IN A BOOK THAT HE COULD PREDICT THE TEMPERATURE BASED ON THE NUMBER OF TIMES A CRICKET CHIRPS PER MINUTE 4O TEST THIS THEORY HE RECORDS CRICKET CHIRPS AND THE TEMPERATURE FOR SEVERAL NIGHTS A $OES THE DATA THAT *ULIAN COLLECTS REPRESENT A Linear FUNCTION %XPLAIN HOW YOU KNOW 9ES THE DATA SET IS Linear 0 OSSIBLE ANSWER 4HE DIFFERENCE BETWEEN ORDERED PAIRS IS PROPORTIONAL ??? ??? ?? B *ULIAN WROTE THE EQUATION 4 C ?? TO CALCULATE THE TEMPERATURE S 4 D BASED ON C CHIRPS PER MINUTE 'RAPH THE EQUATION ON A Graphing CALCULATOR &IND THE C AND 4 INTERCEPTS C INTERCEPT 4 INTERCEPT C !

6 BOUT HOW MANY TIMES PER MINUTE SHOULD A CRICKET CHIRP AT & 'RAPH EACH EQUATION )DENTIFY THE POLYGON FORMED BY THE INTERSECTING LINES 'IVE THE COORDINATES OF THE VERTICES OF THE POLYGON Y X Y X Y Y X 4 RAPEZOID T E T E T E T E #AR -ILEAGE 2 ECORDS$ISTANCE MI 'AS GAL #RICKET #HIRPS VS 4 EMPERATURE#HIRPS PER MIN 4 EMPERATURE & XY #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved 5SE INTERCEPTS TO SKETCH THE GRAPH OF THE FUNCTION X Y 4HE X INTERCEPT IS WHERE THE GRAPH CROSSES THE X AXIS 4O FIND THE X INTERCEPT SET Y AND SOLVE FOR X X Y X X X 4HE Y INTERCEPT IS WHERE THE GRAPH CROSSES THE Y AXIS 4O FIND THE Y INTERCEPT SET X AND SOLVE FOR Y X Y Y Y Y 0 LOT THE POINTS AND $RAW A LINE CONNECTING THE POINTS &IND THE INTERCEPTS AND GRAPH EACH LINE ,i i>V 'RAPHING ,INEAR &UNCTIONS ,%33/. X Y A X S D X INTERCEPT B S D Y Y INTERCEPT X Y A X S D X INTERCEPT B S D Y Y INTERCEPT 4HE Y INTERCEPT OCCURS AT THE POINT S D 4HE X INTERCEPT OCCURS AT THE POINT S D XY X YX Y 7912/7/05 6:36:37 PM12/7/05 6:36:37 PMCopyright by Holt, Rinehart and Winston.)

7 80 Holt Algebra 2 all rights reserved .#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved 7 RITE EACH FUNCTION IN SLOPE INTERCEPT FORM 5SE M AND B TO GRAPH ,i i>V 'RAPHING ,INEAR &UNCTIONS CONTINUED ,%33/.Y MX B IS THE SLOPE INTERCEPT FORM M REPRESENTS THE SLOPE AND B REPRESENTS THE Y INTERCEPT 5SE THE SLOPE AND THE Y INTERCEPT TO GRAPH A Linear FUNCTION 4O WRITE Y X IN SLOPE INTERCEPT FORM SOLVE FOR Y Y X X X Y X Y ??? X ?? ?? Y ?? X #OMPARE Y ?? X TO Y MX B M ?? SO THE SLOPE IS ?? B SO THE Y INTERCEPT IS X Y A Y X B M C B Y X ?? A Y ?? X B M ?? C B XY X Y X Y #OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/. > i }i)NTERCEPTS AND 4 RIANGLES %VERY Linear EQUATION IN X AND Y CAN BE WRITTEN IN THE FORM AX BY C WHERE A AND B CANNOT BOTH BE )F A B AND C ARE NOT ZERO THEN THE GRAPH IS A LINE THAT CROSSES BOTH THE X AXIS AND THE Y AXIS AT POINTS OTHER THAN THE ORIGIN SUCH AS IN THE DIAGRAM AT RIGHT 9OU CAN USE THE EQUATION OF A LINE TO FIND THE AREA OF A TRIANGLE A B AND C ARE NONZERO CONSTANTS AND AX BY C 3 HOW THAT THE X INTERCEPT OF THE GRAPH IS C ?))

8 ? A AND THAT THE EQUATION Y INTERCEPT IS C ?? B 4O FIND THE X INTERCEPT LET Y AX BY C AX B S D C AX C X C ?? A 4O FIND THE Y INTERCEPT LET X AX BY C A S D BY C BY C Y C ?? B %XPLAIN WHY A B AND C MUST BE NONZERO IN ORDER TO FORM A TRIANGLE WHOSE SIDES ARE THE LINE REPRESENTED BY THE EQUATION AX BY C AND THE COORDINATE AXES 0 OSSIBLE ANSWER )F ANY OF A B OR C ARE THEN THERE IS NO TRIANGLE SINCE THE LENGTHS OF TWO OF THE SIDES ARE C ?? B AND C ?? A A A B AND C ARE POSITIVE NUMBERS 7 RITE A FORMULA FOR THE AREA OF THE TRIANGLE FORMED BY THE GRAPH OF AX BY C AND THE COORDINATE AXES ! C ???? AB B &IND THE AREA OF THE RIGHT TRIANGLE FORMED BY THE GRAPH OF X Y AND THE COORDINATE AXES SQUARE UNITS ! TRIANGLE WHOSE SIDES ARE THE GRAPH OF A LINE AND THE COORDINATE AXES HAS AN AREA OF SQUARE UNITS 7 RITE AN EQUATION OF THE FORM AX BY C FOR THE HYPOTENUSE OF THE TRIANGLE 0 OSSIBLE ANSWER X Y 3 OLVE A $RAW THE GRAPH OF A LINE WITH X INTERCEPT AND Y INTERCEPT B &IND THE CONSTANTS A B AND C FOR THE LINE A B C C 7 RITE THE EQUATION FOR THE LINE X Y D 7 RITE THE EQUATION IN SLOPE INTERCEPT FORM 7 HAT IS THE SLOPE OF THE LINE Y ?

9 ?? X ??? E 7 HAT IS THE AREA OF THE RIGHT TRIANGLE FORMED BY THE LINE AND THE COORDINATE AXES SQUARE UNITSXY " ] VL ] V>#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/.* L i - }'RAPHING ,INEAR &UNCTIONS 3 OLVE .ATHAN MADE A TABLE TO RECORD THE BALANCE IN HIS SAVINGS ACCOUNT WHEN HE MADE A DEPOSIT EVERY OTHER MONTH 3 AVINGS "ALANCE-ONTH "ALANCE )S THIS DATA SET Linear (OW DO YOU KNOW .O 0 OSSIBLE ANSWER THE RATE OF CHANGE IS NOT CONSTANT 3 ALLY RUNS A LANDSCAPE SERVICE BUSINESS 4HE TABLE SHOWS HER FEE SCHEDULE ,ANDSCAPE 3 ERVICES4 IME H 0 RICE A 7HY IS THE DATA SET Linear "ECAUSE THE RATE OF CHANGE IS CONSTANT B &IND THE SLOPE OF THE LINE THAT PASSES THROUGH THE POINTS C 'RAPH THESE DATA D %STIMATE THE COST FOR HOURS OF LANDSCAPE SERVICES #HOOSE THE LETTER FOR THE BEST ANSWER *AN BUILT A SKATEBOARD RAMP FROM HER BACK PORCH TO THE GROUND 4HE PORCH IS INCHES ABOVE THE GROUND 4HE RAMP EXTENDS FEET FROM THE BASE OF THE PORCH &IND THE SLOPE OF THE RAMP !))

10 # " $ 7 HEN 2 AFIQ LEFT HOME ON A BUSINESS TRIP HE NOTED THAT THE ODOMETER ON HIS CAR READ (E DROVE H MIN AND THEN NOTED THAT THE ODOMETER READ &IND HIS AVERAGE SPEED IN MILES PER HOUR ! # " $ XY 4 IME H 0 RICE ,ANDSCAPE 3 ERVICES#OPYRIGHT BY (OLT 2 INEHART AND 7 INSTON (OLT !LGEBRA !LL rights reserved ,%33/.$EFINITION! FUNCTION WITH A CONSTANT RATE OF CHANGE IS CALLED A Linear FUNCTION F S X D MX BM IS THE SLOPE B IS THE Y INTERCEPT &ACTS4HE GRAPH OF A Linear FUNCTION IS ALWAYS A STRAIGHT LINE 9OU CAN USE THE EQUATION OF A Linear FUNCTION TO FIND ITS SLOPE AND INTERCEPTS Y MX B %XAMPLE,INEAR FUNCTION X Y 3 LOPE INTERCEPT FORM OF THE Linear FUNCTION Y X 3 LOPE Y INTERCEPT 5 SEFUL (INTS9OU CAN USE ANY TWO POINTS ON A LINE TO DRAW ITS GRAPH 4HE INTERCEPTS GIVE YOU TWO POINTS ON THE LINE 9OU CAN ALSO GRAPH A LINE USING ITS SLOPE AND ONE POINT ON THE LINE #OMPLETE THE TABLE,INEAR &UNCTION3 LOPE ))))