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 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:

1. **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 \( x \).

2. **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.

3. **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 \( x \).

4. **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.