Podcast
Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App
Questions and Answers
What is the mathematical form of a direct variation relationship?
What is the mathematical form of a direct variation relationship?
- $y = kx^2$
- $y = kx$ (correct)
- $y = k + x$
- $y = rac{k}{x}$
Which characteristic is true for direct variation?
Which characteristic is true for direct variation?
- The graph is a hyperbola.
- If $x$ decreases, $y$ also decreases.
- If $x$ increases, $y$ also increases. (correct)
- The relationship has no constant of variation.
Which equation represents an inverse variation?
Which equation represents an inverse variation?
- $y = kx$
- $y = rac{k}{x}$ (correct)
- $y = kx^2$
- $y = k + x$
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 $x = 2$?
Signup and view all the answers
What type of graph represents an inverse variation?
What type of graph represents an inverse variation?
Signup and view all the answers
Flashcards are hidden until you start studying
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 ).
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
