Questions and Answers
What is a direct variation graph?
A straight line that goes through the origin.
What is a direct variation table?
The ratio y/x is the same for every pair of points.
What is the direct variation equation?
y=mx or y=kx
What does linear mean?
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What is slope?
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What are quadrants?
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How do you get k or m using a table?
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Direct variation is the same as what?
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What is the slope formula?
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If y varies directly with x, what is the equation when y is 12 and x is 4?
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If y varies directly with x, what is the equation when y is 35 and x is 7?
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What is the dependent variable in the relationship where the quantity of food a dog eats varies directly to its weight?
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What is the independent variable in the relationship where the quantity of food a dog eats varies directly to its weight?
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What is the constant of variation for Heather’s weekly pay if her pay is $174 for 24 hours of work?
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If Heather’s pay is $174 for 24 hours of work, what would her pay be for 40 hours?
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If Eduardo counted ten seconds between seeing lightning and hearing thunder and the distance varies directly, how far away was the lightning after counting 4 seconds?
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If a rabbit can cover 7 miles in 12 minutes, how long would it take to cross 220 miles?
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What is the approximate constant of variation for a rabbit that can cover 7 miles in 12 minutes?
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Y varies directly to X. True or False?
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X varies directly to Y. True or False?
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Study Notes
Direct Variation Concepts
- Direct variation represents relationships in mathematics where one variable is a constant multiple of another variable.
- A direct variation graph is a straight line that passes through the origin, showing a linear relationship.
- In a direct variation table, the ratio ( \frac{y}{x} ) remains constant for all pairs of points.
Direct Variation Forms
- The equation of direct variation can be expressed as ( y = mx ) or ( y = kx ), where ( m ) or ( k ) is the constant of proportionality.
- Direct variation is equivalent to a proportional relationship, indicating linear relationships between the variables.
Linear Properties
- Linear functions are represented graphically as straight lines with a constant slope.
- Slope reflects the steepness of a line, often described as the rate or constant of proportionality (( k )) in direct variation.
Analyzing Direct Variation
- To find the constant of variation (( k ) or ( m )) using a table, divide ( y ) by ( x ) for any point on the graph.
- Quadrants are the four sections in the coordinate plane that help locate points in a Cartesian system.
Application Examples
- When analyzing direct relationships:
- In Heather's case, her pay of $174 for 24 hours results in a constant of variation of $7.25 per hour.
- For a rabbit traveling 220 miles, with a speed of 7 miles in 12 minutes, the time to cross is approximately 377 minutes, indicating distance varies directly with time.
Variables in Direct Variation
- The dependent variable is the quantity affected by changes, while the independent variable is the one that influences it.
- In the dog food scenario, the quantity of food consumed is the dependent variable, while the dog's weight serves as the independent variable.
True/False in Direct Variation
- "Y varies directly with X" is true, illustrating direct variation.
- "X varies directly with Y" is false; direct variation is not symmetric.
Additional Calculations
- When calculating direct variations, determine the equation based on provided values (e.g., ( y = 3x ) if ( y ) is 12 when ( x ) is 4).
- Use similar methods for other scenarios like counting seconds between lightning and thunder to find distances, reflecting on direct variation rules to derive answers.
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Description
Test your knowledge of direct variation concepts through these flashcards. Each card explores definitions and key terms related to direct variation graphs, tables, equations, and slopes in Algebra I. Perfect for students looking to reinforce their understanding of linear relations.
