Question

Using the equation `C=5+12x,`which of the following statements could be a correct interpretation of the coefficient of a term?

Answer 1

In the equation \( C = 5 + 12x \), the coefficient of the term \( x \) is 12. This coefficient can be interpreted in several ways depending on the context of the equation. Here are a few possible interpretations:

1. **Rate of Change**: The coefficient 12 can represent a rate of change of \( C \) with respect to \( x \). Specifically, for each unit increase in \( x \), \( C \) increases by 12 units.

2. **Slope**: If this equation represents a linear relationship on a graph, the coefficient 12 indicates the slope of the line. This means that for every unit increase in \( x \), the value of \( C \) increases by 12, reflecting a positive linear relationship.

3. **Influence on the Dependent Variable**: The coefficient 12 signifies how strongly the variable \( x \) influences the dependent variable \( C \). A larger coefficient indicates that changes in \( x \) have a more significant impact on \( C \).

4. **Expected Increase**: In a situation where \( x \) might represent something like quantity sold or hours worked, the coefficient indicates that for every unit of increase in \( x \), we expect an increase of 12 in the value of \( C \).

In summary, the coefficient 12 in the equation \( C = 5 + 12x \) could be interpreted as a rate of change, slope, influence of \( x \), or expected increase in \( C \) for each unit change in \( x \). The exact interpretation would depend on the specific context in which the equation is applied.