Question

equations of a line tutorial
part c
now that you have an idea of how much money the baseball team will collect and how much it will spend, youre ready to write an equation modeling the situation. write an equation representing the profit made on the car wash in dollars, y, in terms of the number of cars washed, x, after expenses.
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part d
you now have an equation to model the finances of the car wash. what is the value of the profit when the baseball team washes 0 cars? what point represents this value? what does the y - value of this point mean in terms of the problem?
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part e
the baseball team will break even when the amount of money it has received equals the amount of money it spent. in other words, the team breaks even when the profit is equal to zero. how many cars does the baseball team have to wash to break even? what point represents this value? what does the x - value of this point mean in terms of the problem?

Explanation:

To solve these parts, we typically assume some common values for car wash scenarios (e.g., revenue per car, fixed costs) since they aren't provided. Let's assume:

Part C: Equation for Profit

Profit (\( y \)) = Revenue - Expenses.

• Suppose the team earns \( \$5 \) per car (revenue per car) and has fixed expenses of \( \$100 \).
• Revenue = \( 5x \) (where \( x \) = number of cars).
• Expenses = \( 100 \) (fixed).
• Profit: \( y = 5x - 100 \).

Part D: Profit When \( x = 0 \)

Substitute \( x = 0 \) into the profit equation:
\( y = 5(0) - 100 = -100 \).

• The point is \( (0, -100) \).
• The \( y \)-value (\( -100 \)) means the team loses \( \$100 \) (incurs fixed expenses) when washing 0 cars.

Part E: Break - Even (Profit = 0)

Set \( y = 0 \) and solve for \( x \):
\( 0 = 5x - 100 \)
\( 5x = 100 \)
\( x = 20 \).

• The point is \( (20, 0) \).
• The \( x \)-value (20) means the team must wash 20 cars to cover all expenses (break even).

Answer:

s (Using Assumed Values):

• Part C: \( \boldsymbol{y = 5x - 100} \) (adjust based on actual revenue/expenses).
• Part D: Profit = \( \boldsymbol{-100} \); Point = \( \boldsymbol{(0, -100)} \); \( y \)-value = Loss of \( \$100 \) at 0 cars.
• Part E: Cars to break even = \( \boldsymbol{20} \); Point = \( \boldsymbol{(20, 0)} \); \( x \)-value = 20 cars to break even.

(Note: Replace \( 5 \) (revenue per car) and \( 100 \) (fixed expenses) with the actual values from the problem’s context if provided.)