Question

a software company is throwing a dinner party for its employees at a hotel. mr. spencer recorded the prices for two different catering companies in the table below.

\

$$\begin{tabular}{|c|c|c|} \\hline company & initial payment & rate per employee \\\\ \\hline fantastic catering & \\$135 & \\$12 \\\\ \\hline devoted catering & \\$0 & \\$15 \\\\ \\hline \\end{tabular}$$

create a system of linear equations that describes the total cost, \\(y\\), to cater a dinner party for \\(x\\) employees. write the slope-intercept form of the equation for fantastic catering followed by the slope-intercept form of the equation for devoted catering. do not include dollar signs in the equations.

Explanation:

⚡ Using what you learned: introduction to systems of equations

Step 1: Equation for Fantastic Catering

The total cost \( y \) consists of a one-time initial payment (the y-intercept) and a rate per employee (the slope).

• Initial Payment: \( 135 \)
• Rate Per Employee: \( 12 \)

$$ y = 12x + 135 $$

Step 2: Equation for Devoted Catering

• Initial Payment: \( 0 \)
• Rate Per Employee: \( 15 \)

$$ y = 15x $$

Answer:

$$
LATEXBLOCK0
$$