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Questions and Answers
What is the mathematical form of a direct variation relationship?
What is the mathematical form of a direct variation relationship?
Which characteristic is true for direct variation?
Which characteristic is true for direct variation?
Which equation represents an inverse variation?
Which equation represents an inverse variation?
If $k = 8$ in an inverse variation, what is the value of $y$ when $x = 2$?
If $k = 8$ in an inverse variation, what is the value of $y$ when $x = 2$?
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What type of graph represents an inverse variation?
What type of graph represents an inverse variation?
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Study Notes
Variation
Direct Variation
- Definition: A relationship where one variable is a constant multiple of another.
- Mathematical Form: ( y = kx )
- Where ( k ) is the constant of variation.
- Characteristics:
- If ( x ) increases, ( y ) increases (and vice versa).
- The graph is a straight line passing through the origin (0,0).
- Example:
- If ( k = 3 ), then ( y = 3x ). For ( x = 2 ), ( y = 6 ).
Inverse Variation
- Definition: A relationship where one variable increases as the other decreases.
- Mathematical Form: ( y = \frac{k}{x} )
- Where ( k ) is the constant of variation.
- Characteristics:
- If ( x ) increases, ( y ) decreases (and vice versa).
- The graph is a hyperbola.
- Example:
- If ( k = 12 ), then ( y = \frac{12}{x} ). For ( x = 3 ), ( y = 4 ).
Direct Variation
- A relationship exists where one variable is directly proportional to another.
- Represented mathematically as ( y = kx ), with ( k ) as the constant of variation.
- If ( x ) increases, ( y ) also increases, maintaining a consistent ratio.
- The graph of a direct variation is a straight line that intersects the origin (0,0).
- Example of direct variation: If ( k = 3 ), then the equation becomes ( y = 3x ). For an input of ( x = 2 ), the output is ( y = 6 ).
Inverse Variation
- A relationship exists where one variable increases while the other decreases.
- Mathematically expressed as ( y = \frac{k}{x} ), with ( k ) being the constant of variation.
- Inverse variation means that as ( x ) increases, ( y ) correspondingly decreases, and vice versa.
- The graphical representation of inverse variation forms a hyperbola.
- Example of inverse variation: If ( k = 12 ), then the equation becomes ( y = \frac{12}{x} ). For an input of ( x = 3 ), the output is ( y = 4 ).
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Description
Explore the concepts of direct and inverse variation in mathematics. This quiz covers definitions, mathematical forms, characteristics, and examples of both types of variation. Test your understanding of how these relationships between variables work.
