$1.)(10$ pts$)$ Using the appropriate transformation $($change of variables$),$ compute the integral

${}_R\frac{y-4x}{y+4x}dA,$

where $R$ is the region in the $xy-$plane enclosed by the lines $y=4x,y=4x+2,y=2-4x,$ and $y=5-4x.$

$($You do not need to sketch anything, but you need to display the equations for your transformation, the calculation of the Jacobian, and the calculation of the integral in the new coordinates$).$