Sales man decides his sale price initially as marked price MP and gives a discount D%. Let us say the salesman's final decided selling price (excluding tax) is P.

Tax amount = Sales_tax% * P = x

If we say Sales_tax % is fixed as per laws, let us call it C%.

x = C% * P = P * C/100

=> P = 100 x /C

Retail Sale price = RP = P + tax amount = 100 x /C + x

* y = x (100/C+1) = (100+C) x / C*

This is the linear relationship between the sales tax amount and the retail price.

When x = $77.76, y = $972,

=> 100/C + 1 = 972/77.76 = 12.5

=> C = 100 / 11.5 = 8.695

Hence **y = 12.5 x** is the relationship between sales tax and retail price.

with sales tax percentage being C = 8.695%

sales tax = $92.34 = x

=> retail price = y = 12.5 * $92.34 =** $ 1, 154.25**