Question

Fiona wrote the linear equation y = 2/5 x – 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s?
A. x – 5/4y = 25/4
B. x – 5/2y = 25/4
C. x –5/4 y = 25/2
D. x – 5/2y = 25/2

Answer 1

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

$x-\frac{5}{2}y= \frac{25}{2}$

Answer 2

y = 2/5 x – 5 ==> 5/2y = x - 25/2 (times 5/2) ==> x - /2y = 25/2

Answer: x –5/2 y = 25/2 or D.