Answer:
"What are the different kinds of variation?"
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1. Direct variation
- It is a relationship between two variables, x, and y, that can be written as y = kx where k ≠ 0.
- It means that as x increase, y increase, and as x decreases, y decreases.
y = kx
“y varies directly as x”
“y is directly proportional to x”
“y is proportional to x”
*k represents the constant of variation (which relates the two variables)
- For finding the constant (k):
[tex]k=\frac{y}{x}[/tex]
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2. Inverse variation
- It is a relationship between two variables, x, and y, that can be written as [tex]y=\frac{k}{x}[/tex] where k ≠ 0.
- For two quantities with inverse variation, as one quantity increases, the other quantity decreases.
[tex]y=\frac{k}{x}[/tex]
“y varies inversely as x”
“y is inversely proportional to x”
*k represents the constant of variation (which relates the two variables)
- For finding the constant (k):
[tex]k=xy[/tex]
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3. Joint Variation
[tex]y=kxz[/tex]
“y varies jointly as x and z”
- For finding the constant (k):
[tex]k=\frac{y}{xz}[/tex]
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4. Combined Variation
- It is a combination of direct and inverse variation.
- The statement “ y varies directly as x and inversely as z” means [tex]y=\frac{kx}{z}[/tex], where k is the constant of variation.
[tex]y=\frac{kx}{z}[/tex]
“y varies directly as x and inversely as z”
- For finding the constant (k):
[tex]k=\frac{yz}{x}[/tex]
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I hope it helps :).
