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TYPES OF RELATIONS

This resource explores linear relations, particularly focusing on constant functions and direct variation. A constant function is exemplified by the price of fuel, which remains steady at 98.9 cents per litre regardless of the volume purchased. In contrast, direct variation is illustrated through the cost of apples, priced at $2.50 per kilogram, where the cost varies directly with the amount purchased. The materials include tables of values and graphs, emphasizing the rate of change, rules, and their graphical representations.

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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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