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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:

Month Hours of Maintenance Service Maintenance Costs

January $560$ $ $5,253$

February $4804,220$

March $2702,730$

April $4504,270$

May $3303,050$

June $4604,140$

July $3503,010$

August $4103,510$

September $4904,050$

October $4003,280$

November $3703,230$

December $3503,040$

Total $4,920$ $ $43,783$

Average $410$ $ $3,649$

Required:

$1.$ 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.