MPM IDI
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U5
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D4
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December 19, 2016
Direct Variation.notebook
Unit 4
Modelling Equations
(Chapter 5 in textbook!)
Day 1
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Direct Variation
What’s the relaitonship?
What is direct variation?
Problems where if one thing rises or lowers
the other thing also rises or lowers
accordingly.
How does this apply to our ice cream
exam pie?
ice
Vrie
i+/i
1J *n1xiauuie
I
MPM IDI
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US
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December 19, 2016
D4 Direct Variation.notebook
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Direct variation formula:
yrnx
m is the constant of variation(tells you how
y varies with x aka slope)
x and y are the two things
The number of customers that an ice cream cart gets
varies directly with the temperature. If there are 50
customers when the temperature is 60 degrees
Fahrenheit, how many customers will there be if the
temperature is 90 degrees Fahrenheit?
Since we know this so direct variation We hove the equation
yzmx.
where
o we car
SUDSI
X:
t’. p
and y: 1oi tuS IYiQY
lu ;e end ;or for the cor:ston I of ;ariution
once we hove the constant of variation(oko slope) we con
substitute the given temperature and solve for the number
of customers
temp
__
:::
# of customers
5(9D)
60
90
S
75
(0
t•75
2
December 19, 2016
MPM IDI - U5 - D4 - Direct Variation.notebook
Direct Variation graph
graph the data from the ice cream problem.
temperatun
V
cc
60
50
90
75
Sc
what do you notice
about the y intercept?
20
77-
tttf
70
-
ii
80
(ô,ôJ
Is
Ct)
?
0
I ih Ibliowing table shows the relation heLween the
distance and the I jaw on a hike ride.
a) Graph the table in sheets or
lime (mitt) Distance (kin) desmos, whot is the y-intercept?
I
02
It)
2
15
3
20
4
25
is
.1
5
a1c+t
b) Is the bike going at a
constant speed?
-€Ij
Gj’\A
5
p
a
z-zr
c) What speed is the bike going?
s-I
d) What equation models this bike ride?
=
e) How long will it toke to ride 5km?
5
2Sc
o.
3
MPM IDI - U5 - D4 - Direct Variation.notebook
December 19, 2016
Ft 2
Paula works as a lifeguard. Her total earnings vary
directly with the number of hours she works. She
earned $120 for 15 hours of work last week.
a) Find the equation that relates her wages (w) with the
number of hours worked (h).
i
(PC.4
V 04 l’a’—
rn7-
b)
How much does Paula earn for 22 h of work?
LUc)
How many hours does Paula need to work to earn $76?
d) Graph the relation in desmos. What is the y
intercept?
oU,ref
Is
SjPU_ I-I-
La1
ou,’cv4i’c’
[lie cost olbananas vades directly with (he mass in kg.
Ifbananas cost SI .25/kg.
a) Make a table of values.
Mass (kg.)
b) Graph the Relation
Cost(S)
4,
0
1,25
1
c
3
t
c)
Write an equation in the form of y
kvm
d)
(.15
Cr
j25n
Use the
to estimate how many kgs of bananas
could be bought for $5.75.
fvi’X
e)
mx
+sk&
Use the equation to estimate how many kys of bananas
could be bought for $5.75.
75r 1zc
4
December 19, 2016
MPM 101 - U5 - D4 - Direct Variation.notebook
Summarizing Direct Variation;
Equation
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Looks Like...
Example
y:mx
C: 3.20g
posses through the
origin
Graph
0
12345
Time (hours)
Today’s Practice Questions:
Pg 242 244 # I
9, 10, 12, 14
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I
5