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 Consider the amount of fuel purchased and

the price per litre. (Gas is 98.9 cents per litre)

Table of ValuesAmount (L)

1 5 10 15 … x

Price per Litre (¢)

98.9

RELATION 1 Consider the amount of fuel purchased and

the price per litre. (Gas is 98.9 cents per litre)

Table of ValuesAmount (L)

1 5 10 15 … x

Price per Litre (¢)

98.9 98.9 98.9 98.9 … 98.9

GRAPH ..straight line parallel to x-axis

Amount (L)

Price per Litre (¢)

0 5 10 15

100

75

50

25

Price of Fuel

RULEThe rule is:

cost per litre = 98.9 ¢The rule is y = 98.9 ¢

Table of ValuesNo matter what the x value is..the

y value always stays the SAME

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

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

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

RELATION 2 – DIRECT VARIATION The cost of apples is $2.50 per kg.

Independent variable: # of kg of apples

Dependent variable: cost ($)

TABLE OF VALUES

Amount (kg)

0 1 2 5 … x

Cost ($)

TABLE OF VALUES

Number of kg purchased

0 1 2 5 … x

Cost ($) 0 2.50 5.00 12.50

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 xRule for this question: y=2.50x

Number of kg purchased

0 1 2 5 … x

Cost ($) 0 2.50 5.00 12.50 2.50 xRULE

GRAPH

Amount (kg)

Cost ($)

0 1 2 3

10.007.505.002.50

Cost of Apples

DIRECT VARIATIONThere 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

WORK ON ZERO AND DIRECT RELATIONS WorkbookPage 116 #8,9

Text #2Page 101 #1Page 102 #4a-h, #5Page 103 #6, 7Page 104 #9 (find the rate of change first then

write it in the rule y = ax

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