we have
[tex]y=\frac{2}{5}x-5[/tex]
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) [tex]x-\frac{5}{4}y= \frac{25}{4}[/tex]
Multiply by [tex]4[/tex] both sides
[tex]4x-5y= 25[/tex]
[tex]5y=4x-25[/tex]
Divide by [tex]5[/tex] both sides
[tex]y=\frac{4}{5}x-5[/tex]
therefore
the case A) is not equal to Fiona's equation
case B) [tex]x-\frac{5}{2}y= \frac{25}{4}[/tex]
Multiply by [tex]4[/tex] both sides
[tex]4x-10y= 25[/tex]
[tex]10y=4x-25[/tex]
Divide by [tex]10[/tex] both sides
[tex]y=\frac{2}{5}x-2.5[/tex]
therefore
the case B) is not equal to Fiona's equation
case C) [tex]x-\frac{5}{4}y= \frac{25}{2}[/tex]
Multiply by [tex]4[/tex] both sides
[tex]4x-5y= 50[/tex]
[tex]5y=4x-50[/tex]
Divide by [tex]5[/tex] both sides
[tex]y=\frac{4}{5}x-10[/tex]
therefore
the case C) is not equal to Fiona's equation
case D) [tex]x-\frac{5}{2}y= \frac{25}{2}[/tex]
Multiply by [tex]2[/tex] both sides
[tex]2x-5y= 25[/tex]
[tex]5y=2x-25[/tex]
Divide by [tex]5[/tex] both sides
[tex]y=\frac{2}{5}x-5[/tex]
therefore
the case D) is equal to Fiona's equation
the answer is
[tex]x-\frac{5}{2}y= \frac{25}{2}[/tex]
