This situation represents a linear function.
To understand why, consider the relationship between the number of quarters and the total number of dollars. Each quarter is worth 0.25 dollars, and the total number of dollars can be calculated by multiplying the number of quarters (let's denote it as \( q \)) by 0.25. This can be represented by the equation:
\[ d = 0.25q \]
where \( d \) represents the total number of dollars and \( q \) represents the number of quarters.
This equation is of the form \( d = mx + b \), where \( m \) is the slope (in this case, 0.25), and \( b \) is the y-intercept (which is 0 when there are no quarters).
The key characteristics of a linear function are that it has a constant rate of change (the slope) and graphs as a straight line. In this case, for every additional quarter added, the total amount of dollars increases by a constant rate of 0.25.
Therefore, since there is a constant rate of change, the relationship between quarters and dollars is linear.