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.
Company Initial Payment Rate Per Employee
Fantastic Catering $135 $12
Devoted Catering $0 $15

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.

Answer 1

We are given table for the prices for two different catering companies.

Company Initial Payment           Rate Per Employee

________________________________________

$135                                         $12

        $0                                           $15

We know, slope-intercept form of a linear equation:

y= mx+ b.

Where m is the slope ( Rate Per Employee with respect to the problem) and b is the y-intercept (Company Initial Payment).

Plugging m= 12 and b= 135 in slope-intercept form y=mx+b to get first equation.

y = 12x +135.

Plugging m= 15 and b= 0 in slope-intercept form y=mx+b to get second equation.

y = 15x + 0 or y = 15x.

Therefore, system of equations or Devoted Catering are

y = 12x +135.

y = 15x .