Nation's Capital Fitness, Incorporated, operates a chain of fitness centers in the Washington, D$.$C$.,$ area. The firm's controller is accumulating data to be used in preparing its annual profit plan for the coming year. The cost behavior pattern of the firm's equipment maintenance costs must be determined. The accounting staff has suggested the use of an equation, in the form of $Y=a+bx,$ for maintenance costs. Data regarding the maintenance hours and costs for last year are as follows:

$\backslash$table$[[$Month$,\backslash$table$[[$Hours of$],[$Maintenance$],[$Service$]],\backslash$table$[[$Maintenance$],[$Costs$]]],[$January$,550,$$$5,020],[$February$,480,4,190],[$March$,300,2,820],[$April$,470,4,300],[$May$,320,3,010],[$June$,470,4,120],[$July$,350,3,040],[$August$,450,3,520],[$September$,450,3,980],[$October$,370,3,290],[$November$,370,3,170],[$December$,360,3,050],[$Total$,4,940,$$$43,510],[$Average$,\backslash$bar $(412),$$$3,626]]$

PR $6-38($Algo$)$ Part $1$ Estimate the behavior of the maintenance costs incurred...

Required:

Using the high$-$low method of cost estimation, estimate the behavior of the maintenance costs incurred by Nation's Capital Fitness, Incorporated. Express the cost behavior pattern in equation form.

Note: Round coefficient of $x$ to $2$ decimal places and other answer to the nearest whole dollar amount.

Monthly maintenance cost $=$