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Questions and Answers
Which graph represents a direct variation relationship?
Which graph represents a direct variation relationship?
Which of the following graphs illustrates inverse variation?
Which of the following graphs illustrates inverse variation?
Which graph depicts a non-linear relationship?
Which graph depicts a non-linear relationship?
What type of relationship does Graph d represent?
What type of relationship does Graph d represent?
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Which graph represents a scenario of proportional decay?
Which graph represents a scenario of proportional decay?
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What does an upward trend in the graph of a against b suggest?
What does an upward trend in the graph of a against b suggest?
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In the case of direct variation, what type of graph will you see when plotting a against $b^n$?
In the case of direct variation, what type of graph will you see when plotting a against $b^n$?
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What characteristic of the graph indicates inverse variation?
What characteristic of the graph indicates inverse variation?
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When determining the constant of variation in a direct variation scenario, what does the gradient of the line represent?
When determining the constant of variation in a direct variation scenario, what does the gradient of the line represent?
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Which variation type would typically be graphed with a relation a proportional to $\frac{1}{b}$?
Which variation type would typically be graphed with a relation a proportional to $\frac{1}{b}$?
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Which of the following describes inverse variation?
Which of the following describes inverse variation?
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In the context of height and distance observations, what is typically true about two variables in inverse variation?
In the context of height and distance observations, what is typically true about two variables in inverse variation?
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Which graph representation is indicative of inverse variation?
Which graph representation is indicative of inverse variation?
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For a percentage change calculation involving inverse variation, if variable x decreases by 20%, what happens to variable y if they are inversely related?
For a percentage change calculation involving inverse variation, if variable x decreases by 20%, what happens to variable y if they are inversely related?
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Which of the following pairs of values could represent an inverse variation relationship?
Which of the following pairs of values could represent an inverse variation relationship?
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Study Notes
Variation
- Direct variation: A relationship where one variable increases proportionally with another. If y varies directly with x, then y = kx, where k is the constant of variation. A graph of direct variation will pass through the origin.
- Inverse variation: A relationship where one variable decreases proportionally as another increases. If y varies inversely with x, then y = k/x, where k is the constant of variation . A graph of inverse variation will not pass through the origin.
- Joint variation: A relationship where one variable depends on two or more variables. If z varies jointly with x and y, then z = kxy, where k is the constant of variation.
- Part variation: A relationship where one variable is a combination of two or more quantities, each varying in a different way. For example a fixed cost plus a cost per item.
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Description
Explore the concepts of direct, inverse, joint, and part variation in algebra. This quiz will test your understanding of how different types of variation affect relationships between variables and their graphical representations.
