The formula for the Average Rate of Change (ARC) between two points on a line is given by:

$\text{ARC} = \frac{\Delta C(x)}{\Delta x}$

Where:

• $\Delta C(x)$ is the change in cost.
• $\Delta x$ is the change in the number of units (in this case, units of electricity).

Because this is a linear function, the rate of change is constant, meaning it doesn't vary with different values of $x$. In your case, the rate of change is provided as 0.78 dollars per unit, which implies that for every additional unit of electricity consumed, the bill increases by $0.78.

This constant rate of 0.78 only affects the variable part of the cost, as there is also a fixed charge component that remains the same regardless of usage. As a result, the more electricity you use, the larger the variable portion of the bill becomes due to the cumulative impact of the $0.78 per unit rate.

To summarize:

• Fixed charge: remains constant, unrelated to usage.
• Variable charge: $0.78/unit, directly related to the number of units consumed.

The total bill increases linearly as more electricity is used, with the average rate of change only reflecting the variable cost per unit.

Would you like more details or have any questions?

Related questions:

1. How do you calculate the total cost if the number of units and the fixed charge are known?
2. What is the difference between a linear function and a non-linear function in terms of rates of change?
3. How would you calculate the average rate of change if the cost per unit wasn't constant?
4. How does the fixed charge impact the overall cost compared to the variable charge?
5. Can the average rate of change apply to other utility bills or only electricity?

Tip: When analyzing costs, break down fixed and variable components to understand how consumption impacts total expenses!