The problem you uploaded states:

"The cost $C$ of producing $x$ units is $7.50 per unit plus a $300 one-time expense. Write and graph a formula for this situation."

Formula:

The total cost $C$ is made up of two components:

1. A one-time fixed cost of $300.
2. A variable cost of $7.50 for each unit produced.

This can be written as: $C(x) = 7.50x + 300$ where:

• $C(x)$ is the total cost for producing $x$ units,
• $x$ is the number of units produced,
• $7.50 is the cost per unit,
• $300 is the fixed cost.

Graphing:

The equation $C(x) = 7.50x + 300$ is a linear function, so its graph will be a straight line with:

• Slope: 7.50, indicating the cost increases by $7.50 for each additional unit.
• Y-intercept: 300, which represents the initial fixed cost when no units are produced ($x = 0$).

If you'd like, I can also help you sketch or generate this graph digitally!

Would you like to explore the graph more or have any questions?

Here are 5 related questions to deepen understanding:

1. How would the formula change if the one-time expense was $500 instead of $300?
2. What happens to the graph if the per-unit cost changes to $10?
3. What is the cost for producing 50 units according to the formula?
4. How would the graph look if there were no fixed costs (i.e., $300 is removed)?
5. How does the slope of the line relate to the per-unit cost?

Tip: When graphing linear equations, always identify the slope and y-intercept to easily plot the line!