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TYPES OF RELATIONS

TYPES OF RELATIONS. LINEAR RELATIONS:. the graph is a straight line the rate of change “a” is constant (the rate of change between any 2 points on the line will be the same). RELATION 1 – CONSTANT FUNCTION.

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TYPES OF RELATIONS

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  1. TYPES OF RELATIONS

  2. LINEAR RELATIONS: • the graph is a straight line • the rate of change “a” is constant (the rate of change between any 2 points on the line will be the same)

  3. RELATION 1 – CONSTANT FUNCTION • Consider the amount of fuel purchased and the price per litre. (Gas is 98.9 cents per litre) • Table of Values

  4. RELATION 1 • Consider the amount of fuel purchased and the price per litre. (Gas is 98.9 cents per litre) • Table of Values

  5. GRAPH ..straight line parallel to x-axis Price of Fuel Price per Litre (¢) 100 75 50 25 Amount (L) 0 5 10 15

  6. RULE • The rule is: cost per litre = 98.9 ¢ • The rule is y = 98.9 ¢ Table of Values No matter what the x value is..the y value always stays the SAME

  7. The cost per litre is constant • The rate of change is zero (a = 0) • We call this a ZERO VARIATION relation • The rule is: y = b (constant value) • y = 98.9

  8. DO..WORKBOOK PAGE 107-108 ACTIVITY 2 COST OF BUS RIDEDO..A,B,C,D,E,FPAGE 116 #8PAGE 143 #2TEXTBOOK #1PAGE 153 #4BRING TEXTBOOK #2 FROM NOW ON

  9. RELATION 2 – DIRECT VARIATION • The cost of apples is $2.50 per kg. • Independent variable: number of kg you buy • Dependent variable: cost of buying apples

  10. RELATION 2 – DIRECT VARIATION • The cost of apples is $2.50 per kg. • Independent variable: # of kg of apples • Dependent variable: cost ($)

  11. TABLE OF VALUES

  12. TABLE OF VALUES

  13. TABLE OF VALUES • Cost = 2.50 times the amount of kg purchased • y = 2.50 x dep r.o.c indep Rule for direct y = a x Rule for this question: y=2.50x RULE

  14. GRAPH Cost of Apples Cost ($) 10.00 7.50 5.00 2.50 Amount (kg) 0 1 2 3

  15. DIRECT VARIATION • There is no initial fee (start-up cost) • Values are proportional (you can cross multiply and always get the same answer) • The rule is y = ax (“a” is the rate of change) y is dep var, x is indep. var • The graph is a straight line that passes through the origin

  16. WORK ON ZERO AND DIRECT RELATIONS • Workbook Page 116 #8,9 Text #2 Page 101 #1 Page 102 #4a-h, #5 Page 103 #6, 7 Page 104 #9 (find the rate of change first then write it in the rule y = ax

  17. QUIZ ON RATE OF CHANGE…TAKE OUT A PIECE OF PAPER..PUT YOUR NAME ON IT… • Calculate the rate of change…write coordinates, label, write the formula, solve for the r.o.c 1- (2,10) (6,30) a =5 2- (-2,4) (5,-2) a= -6/7 3.- ( 1,8) (8,8) a= o 4- (26,12) (102,50) a= 38/76 or 1/2 5- (24,4) (12,8) a= -4/12 or -1/3

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