we have
\(y=\frac{2}{5}x-5\)
Let's Isolate the variable y in each of the cases and then compare with Fiona's equation to determine the solution of the problem
case A) \(x-\frac{5}{4}y= \frac{25}{4}\)
Multiply by \(4\) both sides
\(4x-5y= 25\)
\(5y=4x-25\)
Divide by \(5\) both sides
\(y=\frac{4}{5}x-5\)
therefore
the case A) is not equal to Fiona's equation
case B) \(x-\frac{5}{2}y= \frac{25}{4}\)
Multiply by \(4\) both sides
\(4x-10y= 25\)
\(10y=4x-25\)
Divide by \(10\) both sides
\(y=\frac{2}{5}x-2.5\)
therefore
the case B) is not equal to Fiona's equation
case C) \(x-\frac{5}{4}y= \frac{25}{2}\)
Multiply by \(4\) both sides
\(4x-5y= 50\)
\(5y=4x-50\)
Divide by \(5\) both sides
\(y=\frac{4}{5}x-10\)
therefore
the case C) is not equal to Fiona's equation
case D) \(x-\frac{5}{2}y= \frac{25}{2}\)
Multiply by \(2\) both sides
\(2x-5y= 25\)
\(5y=2x-25\)
Divide by \(5\) both sides
\(y=\frac{2}{5}x-5\)
therefore
the case D) is equal to Fiona's equation
the answer is
\(x-\frac{5}{2}y= \frac{25}{2}\)
