Electricity Rates in Florida Florida Power & Light Company...

Electricity Rates in Florida Florida Power \& Light Company supplies electricity to residential customers for a monthly customer charge of $$\$ 7.00$$ plus 8.55 cents per kilowatt-hour for up to 1000 kilowatt-hours (kw-hr). (a) Write a linear equation that relates the monthly charge $C,$ in dollars, to the number $x$ of kilowatt-hours used in a month, $0 \leq x \leq 1000$. (b) Graph this equation. (c) What is the monthly charge for using 200 kilowatthours? (d) What is the monthly charge for using 500 kilowatthours? (e) Interpret the slope of the line.

Electricity Rates in Florida Florida Power \& Light Company supplies electricity to residential customers for a monthly customer charge of $$\$ 7.00$$ plus 8.55 cents per kilowatt-hour for up to 1000 kilowatt-hours (kw-hr).
(a) Write a linear equation that relates the monthly charge $C,$ in dollars, to the number $x$ of kilowatt-hours used in a month, $0 \leq x \leq 1000$.
(b) Graph this equation.
(c) What is the monthly charge for using 200 kilowatthours?
(d) What is the monthly charge for using 500 kilowatthours?
(e) Interpret the slope of the line.

Key Concepts

Linear Equations

Linear equations describe relationships between two variables with a constant rate of change. In the context of utility billing, a linear equation models how the total cost increases as consumption increases, where one term represents constant costs and the other represents the cost per additional unit of consumption.

Fixed and Variable Costs

Fixed costs refer to charges that do not change with the level of usage, while variable costs depend on the amount used. In the monthly billing scenario, the fixed cost is the base charge that is always applied, and the variable cost is calculated by multiplying the cost per kilowatt-hour by the number of kilowatt-hours consumed.

Slope-Intercept Form

The slope-intercept form of a linear equation, expressed as y = mx + b, clearly shows the constant rate of change (slope) and the starting value (y-intercept). This form is particularly useful in understanding how additional usage affects the total cost and in quickly interpreting the billing structure.

Graphing Linear Functions and Interpreting Slope

Graphing a linear function involves plotting the fixed cost at zero usage and using the slope to determine the increase in cost for each unit of usage. The slope in this context represents the cost per kilowatt-hour, indicating the rate at which the bill increases with each extra kilowatt-hour used.

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