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 indicates the rate of change of the variable \( c \) with respect to \( x \).

Here are a few possible interpretations of the coefficient 12:

1. **Rate of Change**: For each unit increase in \( x \), the value of \( c \) increases by 12 units.

2. **Slope of the Line**: If this equation is graphed as a linear equation \( c \) vs. \( x \), the coefficient 12 represents the slope of the line, indicating the steepness of the line.

3. **Incremental Increase**: If \( x \) represents a certain quantity (like hours worked, items sold, etc.), then an increase in that quantity by 1 unit results in an increase in \( c \) of 12 units.

Choose the statement that best reflects these interpretations for your specific context.