Question

the food for lucia’s quinceañera costs $18.50 per person. lucia’s 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. the total cost is a function of the number of guests. what does the initial value represent? the total cost, including the discount the number of guests the cost per guest the amount of the discount in dollars

Explanation:

The equation is in the form \( y = mx + b \), where \( b \) is the initial value (y - intercept). Here, the equation is \( y = 18.5x - 50 \), so the initial value is \(-50\) (or \( b=-50\)). The discount is \$50, and the initial value represents the discount amount (since when \( x = 0 \) (no guests), \( y=- 50\), but in context, the discount is a reduction, so the initial value (the constant term) represents the discount in dollars. Let's analyze the options:

• "the total cost, including the discount" is \( y \), not the initial value.
• "the number of guests" is \( x \), not the initial value.
• "the cost per guest" is the slope (\( 18.5 \)), not the initial value.
• "the amount of the discount in dollars" matches because the \(-50\) is the discount (a reduction of \$50), so the initial value (constant term) represents the discount amount.

Answer:

the amount of the discount in dollars