MPM1DI. Unit 6: Graphing Linear Relations. Name:

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1 MPMDI Unit 6: Graphing Linear Relations Name:

3 MPMDI- Unit 6A: Graphing Linear Relations - Lesson Relations and their Representations Date: A relation is a description of how two quantities are connected. The two quantities that change together are called. One quantit will depend on the other and is called the variable. The other is the variable and is the variable whose values ou choose. A relation can be represented using one or more of the following: In graphing, an ordered pair, (, describes a point on the graph. The data applicable in a relation can be either discrete or continuous. data cannot be broken into smaller parts so the points on the graph are connected with a dotted line. data can be broken down into smaller and smaller parts and still have meaning so the points on the graph are connected with a solid line. E.. A plumber charges a flat fee of $50 plus $35/ h for a service call. a What is the independent variable? b What is the dependent variable? c Write an equation to represent in terms of hours of service. d Complete a table of values for up to 8 hours. e Graph the relation for up to 8 hours. f Identif this relation as linear or non- linear with reasons.

4 E. 2. Not all relations are linear. Look at the relationship between side length and volume of a cube, where side length is measured in cm and volume is measured in cm 3. a What is the independent variable? b What is the dependent variable? c Write an equation to represent the volume of the cube in terms of its side length. d Complete a table of values for this relation. e Graph the relation. f Identif this relation as linear or non- linear with reasons. HW: p. 46 #2ab Equation, Table of Values and Graph required, 3ab, 5 p. 48 #0 Table of Values and Graph also required

5 MPMDI- Unit 6A: Graphing Linear Relations - Lesson Grids For Homework: p Date: #2a #2b #3a #3b

6 #5. #0.

7 MPMDI- Unit 6A: Graphing Linear Relations - Lesson 2 Properties of Linear and Non- Linear Relations Direct Variation: - is a linear relation in which one variable is a multiple of the other - the equation looks like = m - (0,0 is an ordered pair in the table of values and a point on the graph Date: Partial Variation: - is a relation in which one variable is a multiple of the other plus a constant amount. - the equation looks like = m + b - (0,0 is not an ordered pair in the table of values or a point on the graph E.. A fitness club offers two tpes of monthl memberships: Membership A: $4 per visit Membership B: a flat fee of $2 plus $2 per visit a Complete a table of values for 0 to 0 visits for each relation and then graph. i Membership A ii Membership B b Identif this set of data as discrete or continuous with reasons. c Write an equation relating the cost, C, in $ and the number of visits, n, for each membership. d Use the equations to determine the number of visits for which both monthl costs are the same. e Identif each relation as direct or partial variation with reasons.

8 Linear Relation: - equation is of the first degree, the graph is a straight line, and in a table of values the first differences are constant. Non- linear Relation: - equation is not of the first degree, the graph is not a straight line, and in a table of values the first differences are not constant. The first differences, erences between consecutive - values where the differences between consecutive - values is constant. E. 2. a Petri Dish A: Bacteria can double ever 30 minutes in a growth medium. Starting with one bacterial cell, set up a table of values for the growth of this bacterial colon over 2 hours and use first differences to determine if the relation is linear or non- linear. b Petri Dish B: Bacteria are growing more slowl due to an antibiotic in the growth medium. Starting with one bacterial cell, onl 5 new cells are generated ever 40 minutes. Set up a table of values for the growth of this bacterial colon over 2 hours and use first differences to determine if the relation is linear or non- linear. Let represent the time in minutes and let represent the number of bacteria in the colon. Petri Dish A a b Petri Dish B c Graph both relations. HW: p. 5 # base answer on form of equation onl, 2, 3; p. 79 #- 5, 7a, 8a

9 MPMDI- Unit 6: Graphing Linear Relations - Lesson 2 Grids For Homework: p. 5 Date: #2. #3.

11 MPMDI- Unit 6A: Graphing Linear Relations - Lesson 3 Date: Coordinate Geometr in 4 Quadrants To describe the location of points on a plane we use the Cartesian Coordinate Sstem. Definitions: -ais the number line which etends left and right. -ais - the number line which etends up and down. origin - the point where the aes meet ordered pair - a point of the form located on a Cartesian plane -coordinate the number in an ordered pair describing the position of the point. -coordinate - the number in an ordered pair describing the position of the point. quadrant the regions created b the Eample: Plot the following points on the grid below: A(4,3 B(-5, C(-2,-4 D(0,5 E(-2,0 F(6, G(-,4 H(, 2 I( - 3,5 O(0, Which points are in: Quadrant I Describe in which quadrant ordered pairs have the following signs. (+, + Quadrant II (+, - Quadrant III (-, + Quadrant IV (-, - HW : WS #, WS #2 and WS#3

12 MPMDI- Unit 6A: Graphing Relations- Lesson 3 Worksheet # Date: p. 503 # a b 4. a b 2. c d p #3c, 4c, 4 3. c 4. c 4.

13 MPMDI- Unit 6A: Graphing Relations - Lesson 3 Worksheet #2 Date:

14 MPMDI- Unit 6A: Graphing Relations- Lesson 3 Worksheet #3 Date:

15 !"!#$%!"#$%(%*+,-#".%/#"0+*%02+$#3"4%5/0443"%6% % % $(*+,,,,,,,,,,,,,,,,,,,,!"#$%(*+,-.*/+"0,2345#$+26+*0#,$" 7*#$+2+8/0#,$9$+:2#00+$#$04+-,2; = m + b :4+2+m(-.b(/*-02*/34 <=>?>$**/5-*567*68998:5-;<85-3(/*8-7*95-* =! (, 4@( 2, 4 <=>A>=/(<7*(>7/*9(58-2?(@5-;((*+,-.*/+":5765A**-/5*34% B = 2 B =!3 + 4

16 9B =! CB =! 3 <=>D>B8<9**7*68998:5-;(29*86A(90*3(-.;/(<74 D=EFGH?A = G C DE G F C IJK3>?FLM?AB7>@>N?ABO>P>N?DECN?LQJRMF

17 !"!#$%!"#$%(%*+,-#".%/#"0+*%02+$#3"4%5/0443"%6% % % $(*+,,,,,,,,,,,,,,,,,,,, 2#C"S,2I,;+:,2TK3>?FLE?FU M?D>B$CB M?D>9B$CCB M?L>

18 !"!#$%!"#$%(%*+,-#".%02+$#3"45%/0443"%6%783*94-00$%:6% % % $(*+,,,,,,,,,,,,,,,,,,,,

19 !"!#$%!"#$%(%*+,-#".%/#"0+*%02+$#3"4%5/0443"%6% % % $(*+,,,,,,,,,,,,,,,,,,,,!"#$%$(*+,("(-.*/,0#$/*23/(#-$" 45#$#(#-$"6 -.* -#$(*+,(/0.*(23*45.*64/78.*9*.*2/7* :9400*0.*,,,,,,,,,,,,,,,,,;-45/7<.* -#$(*+,(= 2*,,,,,,,,,,,,(7<.*7042*549; -.* -#$(*+,(/0.*(23*45.*64/78.*9*.*2/7* :9400*0.*,,,,,,,,,,,,,,,,,;-45/7<.* -#$(*+,(= 2*,,,,,,,,,,,,(7<.*7042*549; 789:9>9(6..*542248/7?2/7*(99*2(/470@A5/7</7?.*/7*9:*60; /; 4! 3 = 2 <; =!3 + 6

20 /; =! <; = +! >?+,9:@AB:/+CD/<CE<+C:F/+G-$3H5#$I(0J/$IJ#$(*+,(";CK/<+

21 !"!#$%!"#$%(%*+,-#".%/#"0+*%02+$#3"4%5/0443"%6% % % $(*+,,,,,,,,,,,,,,,,,,,,.*#I"L-*>-MN-*O6,9:@AJ:KP B:9/;/$I+; BD9/;/$I<; BE9<;/$I+; BK9+;

23 !"!#$%!"#$%(%*+,-#".%/#"0+*%02+$#3"4%5/0443"%% % % $(*+,,,,,,,,,,,,,,,,,,,,!"#$%(*+,-.$/0#$2-,3.-(4#$.5+.#,$" 6758!9 -.(/0*(0230* *(..*4(6279 :96780*67;6(*;<*02;=.:+,;<.+="#$2-" 3 = = 0 5 >0*.,;2(.$%230*467*(..*4(62769(44*;0*,,,,,,,,,,,,,,,,,230*467*= >0*?(4:*230*/26750*.*0*467*.299*90*(@6969(44*;0*,,,,,,,,,,,,,,,,,,,,,,,,,,,,= 3 A2. = + 2 0*942/*69,,,,,,,,,(7;0*67*.*/69,,,,,,,,,,,,= 5 A2. =! 30*942/*69,,,,,,,,,(7;0*67*.*/69,,,,,,,,,,,,= *=>>.?@ >0*8.(/0230*.*4(627 = m + b!69(9.(680467*560942/*,,,,,,(7;67*.*/,,,,,,= B42/*<*(9:.*9,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,= *+,-C >0*8.*(*.0*<(876:;*23942/*mD *9687E,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,= F467*560(-,"##<"+,-,,,,,,,,,,,,,,,,,,,,,,,,,20*.680= F467*560($%.#<"+,-,,,,,,,,,,,,,,,,,,,,,,,,,20*.680=

24 = m + b= CDEFEH2</4**0* (I4*= CG=.#,$ *+,- 0#$2- = 2! 5 = +0 =! 5 2 =! 3 = 3 CDEHEJ.6*0**G:(627230*467*67"+,-B-#$2-;,>560+.I m = (7; b =! :I m = 7 (7; b = 0 2 CDEJEK9*0*"+,-.$/0#$2-28.(/00* *9+.I = 3! 5 2 :I =! CDEKEL*5.6**(0230* *G:( "+,-B-#$2-;,>(7;8.(/0=.I = 0 :I! 4! 28 = 0 L6@6*MN.$/6*MO

25 !"!#$%!"#$%(%*+,-#".%02+$#3"45%/0443"%%673*84-00$%9:% % % $(*+,,,,,,,,,,,,,,,,,,,,

26 !"!#$%!"#$%(%*+,-#".%02+$#3"45%/0443"%%6%73*84-00$%9% % % $(*+,,,,,,,,,,,,,,,,,,,,

27 !"!#$%!"#$%(%*+,-#".%/#"0+*%02+$#3"4% % % %%%%%%%%%%%%$(*+,,,,,,,,,,,,,,,,,,,,!"#$%(*++(,-. /%0#220"302-4$#$-"#4("#$%0,0"-.%# (" (/00* *.#72-089#2:-+:*02;<=>*6.5*9? 2 #; = 2! 7 7; =! + 4 <;! = 0 5 4; = 2 =65#;#47; =65<;#44; >5-.(/00* *.-"<-$.+:*02;< #; 2! 3 = ; 5 + 4! 0 = 0<; + = 3 4;! + 2 = =>5#;#47; =>5<;#44;

28 3 #; = + 7; =!2 + 5<;!! 4 = 04; + 2 = 0 5 =?5#;#47; =?5<;#44; B5@6(//35(6A*.*/(5./*.926A0(.7*9B>C2.(9*.D5A* A(33(6;BEC/* :*9/*6.*/(5.567 (F5A0*6(//35(6A*< #;G0(590*56;*/*6;*6D(.5(H3*I 7;G0(590*;*/*6;*6D(.5(H3*I <;$*56*0*D(.5(H3*9450J3*9(*:*69K(6; 4.5*(6*L8(5262.0*.*/(5./*.926M9A0(.7*9< 4;-.(/00*.*3(5262.8/2> ((H3* 2D(38*9< C5N0*0*5702(H(3340*6F5AF*;5975D*6HO0* 2 *L8(526 h = 30t! 5t P40*.*t590*5:*569*A26;9 (6;h590*0*57056:*.*9< #; -.(/00*.*3(5262.t = 0 2 t = ((H3* 2D(38*9< 7; Q95670*7.(/0P;**.:56**(A020* ;0*:(R5:8:0*570.*(A0*;HO0*H(33 ;0*5:*5(F*92.*(A00*:(R5:8:0*570 ;0*3*67025:*0*H( *(5.

29 MPMDI- Unit 6A: Graphing Linear Relations - Review Date: Unit 6A Test Review HW: p. 283 #, 2, 5ac* (graph using slope, - intercept method Lesson 6 p. 263 #2i Lessons 6 p. 258 #7ab* Lesson 4 p. 258 #8* Lesson 5 p. 63 #2 Lesson 2 p. 83 #2a, 9, 0* Lesson 2 *grids provided p. 283 #5a and c p. 258 #7 a and b p. 258 #8 p. 83 #0

Section 9.3: Functions and their Graphs

Section 9.3: Functions and their Graphs Section 9.: Functions and their Graphs Graphs provide a wa of displaing, interpreting, and analzing data in a visual format. In man problems, we will consider two variables. Therefore, we will need to