In the equation \( C = 5 + 12x \), the term \( 12x \) represents a linear relationship between \( C \) (the dependent variable) and \( x \) (the independent variable). The coefficient of the term \( x \) is \( 12 \). This coefficient can be interpreted in the following ways:
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Rate of Change: The coefficient \( 12 \) indicates that for every one-unit increase in \( x \), the value of \( C \) increases by \( 12 \) units. This means there is a direct proportionality in the increase of \( C \) concerning \( x \).
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Slope: In the context of a graph, the coefficient \( 12 \) represents the slope of the line if \( C \) is plotted against \( x \). A slope of \( 12 \) means the line rises steeply as \( x \) increases.
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Impact of \( x \): The coefficient can also be interpreted as the impact that changes in \( x \) have on \( C \). Specifically, it quantifies how much \( C \) will change based on changes in \( x \).
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Response Variable: If considering a practical scenario, \( 12 \) could represent a specific quantity or measurement depending on the context of what \( C \) and \( x \) represent (e.g., dollars per hour, miles per hour, etc.).
In summary, the coefficient \( 12 \) signifies the rate of increase of \( C \) with respect to \( x \) and serves as a key indicator of the strength of their relationship.
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