Question

interactive practice: use functions to model linear relationships
the food for lucias quinceañera costs $18.50 per person. lucias abuela helped with the cooking, so the caterers gave a $50 discount. the equation, $y = 18.5x - 50$ can be used to find the total cost, including the discount.
the variable $x$ represents the number of guests.
the variable $y$ represents the total cost, including the discount.
complete the statement.
the? is a function of the?.
options for first?: number of guests, total cost
options for second?: (dropdown, context implies related to x or y)

Explanation:

In a function \( y = f(x) \), \( y \) is the dependent variable (output) and \( x \) is the independent variable (input). Here, the equation is \( y = 18.5x - 50 \), where \( y \) (total cost) depends on \( x \) (number of guests). So the total cost is a function of the number of guests.

Step 1: Identify the relationship

The equation \( y = 18.5x - 50 \) shows that \( y \) (total cost) is calculated based on \( x \) (number of guests).

Step 2: Determine the function relationship

In a function, the dependent variable (which is calculated) is a function of the independent variable (which is the input). Here, total cost (\( y \)) is dependent on the number of guests (\( x \)).

Answer:

The total cost is a function of the number of guests.