LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
LINEAR RELATIONS
are Relations that change at a constant rate
EXAMPLES:
ROBOT RULES
TERMS:
DIRECT VARIATION
CONSTANT OF VARIATION
PARTIAL VARIATION
SLOPE
RISE
RUN
RATE OF CHANGE
FIRST DIFFERENCES
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LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
DIRECT VARIATION
A RELATIONSHIP BETWEEN 2 VARIABLES IN WHICH ONE
VARIABLE IS A CONSTANT MULTIPLIER OF THE OTHER
TIME
DISTANCE
X
Y
1
10
2
20
3
30
4
40
5
50
DISTANCE varies DIRECTLY with TIME, therefore, the
RATIO of the variables does not change....
where k is the constant of variation
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LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
Example:
A family travels 250 km. The distance d, varies directly with the
time t, in hours.
a) Find the equation relating d and t if d=43 and t=0.5
What does the constant of variation represent?
b) Use the equation to determine the length of time required to
reach their final destination.
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LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
4
LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
SUMMARY: DIRECT VARIATION
• graph goes through the POINT ( 0, 0 ) ∴, when x = 0 , y = 0
• the CONSTANT OF VARIATION
k is the rate
• the EQUATION is
5
LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
PARTIAL VARIATION:
• a partial variation has an equation in the form
where "b" represents FIXED or INITIAL value
" m " represents CONSTANT VARIATION -- rate
• graph does NOT go through the point (0 , 0 )
y
10
9
8
7
6
5
4
3
2
1
0
x
1
2
3
4
5
6
7
8
9
10
6
LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
Example:
complete the table of values given that y varies partially with x.
b) Identify the INITIAL value of y and the CONSTANT of
variation. Write an equation in the form
c) Graph the relation
d) Describe the graph
X
Y
0
6
1
9
y
28
26
24
22
20
18
16
2
3
14
15
12
10
8
4
6
4
27
2
0
x
1
2
3
4
5
6
7
8
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LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
Example:
A school is planning an awards banquet. The cost of renting the
facility & hiring serving staff is $675. There is an additional cost of
$12 per person for the meal.
a) Identify the fixed cost & the variable cost
b) Write an equation to represent this relationship
c) Use your equation to determine the total cost if 500 people
attend
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LINEAR RELATIONS GRADE 9.notebook
December 14, 2011
Identify each relation as DIRECT, PARTIAL VARIATION or
NEITHER
Complete the table.
a) Identify the initial value and the constant of variation
b) Write an equation in y=mx + b form
X
Y
0
5
1
10
2
3
20
4
40
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