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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 & \[tex]$135 & \$[/tex]12 \\
\hline
Devoted Catering & \[tex]$0 & \$[/tex]15 \\
\hline
\end{tabular}

Create a system of linear equations that describes the total cost, [tex]y[/tex], to cater a dinner party for [tex]x[/tex] 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.



Answer :

GinnyAnswer
To create the system of linear equations that describes the total cost, [tex]\( y \)[/tex], to cater a dinner party for [tex]\( x \)[/tex] employees, we need to consider the initial payment and the rate per employee for each catering company.

For Fantastic Catering:
- The initial payment is [tex]$135. - The rate per employee is $[/tex]12.

The total cost equation for Fantastic Catering can be represented by the linear equation in slope-intercept form:
[tex]\[ y = 12x + 135 \][/tex]

For Devoted Catering:
- The initial payment is [tex]$0. - The rate per employee is $[/tex]15.

The total cost equation for Devoted Catering can be represented by the linear equation in slope-intercept form:
[tex]\[ y = 15x \][/tex]

Thus, the system of linear equations is:
[tex]\[ y = 12x + 135 \][/tex]
[tex]\[ y = 15x \][/tex]

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