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