The total cost, y for Rosa to go on vacation for x days given by the equation y=A+(H+M)x`, where A represents the airface, H represents the cost per day for the hotel, and M represents the cost the metal. If the relationship between the total cost of the vacation and the number of the days of the vacation is graphed on the xy-plane, what does the slope of the line represents?

Options

A. The total cost daily cost of the hotel and meals
B. The total daily cost of the vacation
C. The total cost of the hotel and meals
D. The total cost of the vacation

Answer

To solve the problem step by step, we will analyze the equation given and determine what the slope of the line represents in the context of the vacation costs.

### Step 1: Understand the equation
The total cost \( y \) for Rosa to go on vacation for \( x \) days is given by the equation:
\[ y = A + (H + M)x \]
where:
- \( A \) = airfare (fixed cost)
- \( H \) = cost per day for the hotel
- \( M \) = cost per day for meals

### Step 2: Identify the components of the equation
In this equation, \( (H + M)x \) represents the variable cost that depends on the number of days \( x \). The term \( A \) is a constant that does not change with the number of days.

### Step 3: Rewrite the equation in slope-intercept form
The slope-intercept form of a linear equation is given by:
\[ y = mx + c \]
where \( m \) is the slope and \( c \) is the y-intercept.

In our equation:
- The slope \( m \) can be identified as \( H + M \).
- The y-intercept \( c \) is \( A \).

### Step 4: Interpret the slope
The slope \( H + M \) represents the total cost incurred per day for the hotel and meals combined. This means that for each additional day \( x \) that Rosa stays on vacation, her total cost \( y \) increases by \( H + M \).

### Conclusion
Thus, the slope of the line represents the total daily cost of the hotel and meals.

### Final Answer
The slope of the line represents the total daily cost of the hotel and meals, which corresponds to option (a).

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