Brendan Holmes Presents:
An Educational Presentation
Direct Variation
• Has no fixed cost.
• Has x and y values.
• Uses the formula:
y=mx, where m is the
Constant of Variation.
• On a graph, it:
- is a straight line
- passes through the origin
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Direct Variation
Example #1
•
•
Patrick Kane and Jonathan
Toews were fighting with
the team mascot, so they
were forced to clean up the
garbage in the stands for
community service.
For every hour that they
cleaned, they needed to
pick up 45 pieces of
garbage. Complete a table
of values to see how much
garbage they had picked up
after 7 hours.
Therefore, they picked up 315 pieces
of garbage after 7 hours.
Hours
(x)
Equation Garbage
(y)
0
1
2
3
4
5
6
7
Y=45(0)
Y=45(1)
Y=45(2)
Y=45(3)
Y=45(4)
Y=45(5)
Y=45(6)
Y=45(7)
0
45
90
135
180
225
270
315
Direct Variation
Example #2
•
•
The Ancaster High
School Triathlon was
accepting donations from
the teams. Each team
gave $34.
Complete a table of
values to see how much
money was raised by 6
teams.
Therefore, $204
was raised by 6
teams.
Teams (x)
Equation
Money in
$ (y)
0
1
2
3
4
5
6
Y=34(0)
$0
$34
$68
$102
$136
$170
$204
Y=34(1)
Y=34(2)
Y=34(3)
Y=34(4)
Y=34(5)
Y=34(6)
Partial Variation
• Has a fixed cost.
• Has x and y values.
• Uses the formula:
y=mx+b, where m is
the Constant of
Variation, and b is the
Fixed Cost.
• On a graph it:
- is a straight line
- Does not pass through
the origin
Partial Variation Example
#1
•
•
A group of kids were selling Kool-Aid
for $1.75 a bottle.They started off
with $14.
Complete the table of values to find
how much money the kids earned if 6
people bought their Kool-Aid.
Therefore, the kids
have earned $24.50 if
6 people bought their
Kool-Aid.
# of Kids
(x)
0
1
2
3
4
5
6
Equation
Y=1.75(0)+14
Y=1.75(1)+14
Y=1.75(2)+14
Y=1.75(3)+14
Y=1.75(4)+14
Y=1.75(5)+14
Y=1.75(6)+14
Money
Earned (y)
$14
$15.75
$17.50
$19.25
$21.00
$22.75
$24.50