Direct variation
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I can…
 Illustrate situation that involves direct
variation;
 Translate a direct variation statement into
relationship between two quantities using
mathematical equation.
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Direct variation
The value of y varies directly with the value of
x if there exist a nonzero constant k such that:
𝒚 = 𝒌𝒙
𝒚
or equivalently = 𝒌
𝒙
The constant k is called the constant of variation
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Writing an equation for direct variation
The fare F of a passenger varies directly as the
distance d of his destination.
The cost C of fish varies directly as its weight w
in kilograms.
The area A of a triangle is proportional to its
height h.
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Example no.1
If y varies directly as x, and y=24 and x=3 find:
(a) the constant of variation
(b) Find y when x=2
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Example no.2
If z varies directly as t, and z = 11 when t = 4 find:
(a) the constant of variation
(b) Find z when t=32
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Example no.3
A worker’s pay check (P) varies directly as
the number of hours (h) worked. For working
20 hours, the payment is 1 000 pesos. Find
the payment for 45 hours of work.
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Example no.4
If y varies directly with x and y = 12
when x = 2, find y when x = 8.
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Example no.5
If 8 oranges cost ₱ 10.40, how many
oranges can be bought for ₱ 33.80?
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Assignment
Write an equation
1. The weight(W) of an object is directly proportional to its
mass (m)
2. The volume (v) of a cylinder varies directly as its height (h)
3. The distance (D) travelled by a car varies directly as its
speed (s)
4. An employee’s salary (S) varies directly as the number of
days (d) he has worked.
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Assignment
Find the constant of variation of the following. Include your solution.
1. y=28 when x=7
2. y=30 when x=8
3. y=0.7 when x=0.4
4. y=0.8 when x=0.5
5. y=400 when x=25
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Assignment
Solve for each of the following: Include your solution
1. If y varies directly as x, and y=8, when x=24, find y when x=6
2. If p varies directly as q, and p=18, when q=6, find p when q=14
3. If a varies directly as b, and a=8, when b=4.5, find a when b=8
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Assignment
Solve the following problems. Write the given, formula and solution.
1.
The service fee (f) of a physical therapist varies directly as the number of
hours (h) of service rendered. A physical therapist charges ₱ 2100 for 3
hours service to the patients in home care. How much would he be paid for
6.5 hours of service.
2. If car covers 102 km in 6.8 liters of petrol, how much distance will it cover
in 24.2 liters of petrol.