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 \( 12 \).

A correct interpretation of the coefficient \( 12 \) could be as follows:

1. Rate of Change: The coefficient \( 12 \) represents the rate of change of \( C \) with respect to \( x \). This means that for every one-unit increase in \( x \), the value of \( C \) increases by \( 12 \) units.

2. Slope: If this equation is graphed on a coordinate system, the coefficient \( 12 \) indicates the slope of the line. It shows how steep the line is, with a positive slope indicating that as \( x \) increases, \( C \) also increases.

3. Sensitivity: The coefficient \( 12 \) could also be interpreted as expressing the sensitivity of \( C \) to changes in \( x \); specifically, it reflects how sensitive \( C \) is to changes in \( x \).

Any of these interpretations would be correct regarding the significance of the coefficient in the context of the equation \( C = 5 + 12x \).