Walks you through step by step how to solve direct variation and inverse variation equations. Shows you now to get the constant of variation. Use the calculator at: https://www.mathcelebrity.com/variation.php

1. Variation Problems
● Variation problems determine a relationship function
between two variables.
● 2 Examples
○ Direct Variation (Relationship)
○ Inverse Variation (Divorce)
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2. Direct Variation Problems
● Vary directly
● Vary as the square of
● Vary as the cube of
● Vary as the square root of
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3. Inverse Variation Problems
● Vary inversely
● Vary inversely as the square of
● Vary inversely as the cube of
● Vary inversely as the square root of
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4. Direct Variation Example
y varies directly as x; y = 36 when x = 4;
Solve for y when x = 6. Direct variation imply a y = kx relationship
Take initial statement: y = 36 when x = 4:
4k = 36 ← We use k for the constant of variation, y = kx
k = 9
This means our variation equation is y = 9x
The problem asks for y when x = 6
Y = 9(6) = 54
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5. Inverse Variation Example
y varies inversely as x; y = 36 when x = 4;
Solve for y when x = 6. Inverse variation imply a y = k/x relationship
Take initial statement: y = 36 when x = 4:
k/4 = 36 ← We use k for the constant of variation, y = k/x
k = 144
This means our variation equation is x = 144/y
The problem asks for x when y = 6
x = 144/6 = 24
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6. Direct Variation Squared Example
y varies directly as the square of x; y = 100 when x = 2;
Solve for y when x = 6. Direct variation imply a y = kx2 relationship
Take initial statement: y = 100 when x = 2:
22k = 100 ← We use k for the constant of variation, y = kx2
4K = 100 → k = 25
This means our variation equation is y = 25x2
The problem asks for y when x = 6
Y = 25(62) = 25(36) = 900
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