Answer-
- [tex]y=18x+200[/tex]
- slope = 18, y-intercept = 200
- Cost of catering for 200 guests is $3800.
Solution-
A caterer charges a $200 fee plus $18 per person served.
Let us assume that
The cost = y
The number person served = x
As $200 is a fixed charge and $18 is a variable charge, so the equation would be,
[tex]y=18x+200[/tex] ----------------------1
The graph of the function is attached below.
Comparing the equation 1 with general slope-intercept form of straight line,
[tex]y=mx+c[/tex]
here,
m = slope = 18
c = y-intercept = 200
Slope means the rate of change or the variation, as the number of person increases the cost increases by an amount of $18, so the slope is 18.
y-intercept is the place on the graph where x = 0, i.e when x is 0 or number of person served is 0, the cost will be $200. It doesn't matter whether any person is being served or not, the caterer will charge $200.
In order to find the cost of catering for 200 guests, putting x = 200 in equation 1,
[tex]y=18(200)+200[/tex]
[tex]y=3600+200[/tex]
[tex]y=3800[/tex]
Therefore, the cost of catering for 200 guests is $3800.
