Question

fiona’s equation
fiona wrote the linear equation ( y = \frac{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?
( \bigcirc x - \frac{5}{4}y = \frac{25}{4} )
( \bigcirc x - \frac{5}{2}y = \frac{25}{4} )
( \bigcirc x - \frac{5}{4}y = \frac{25}{2} )
( \bigcirc x - \frac{5}{2}y = \frac{25}{2} )

Explanation:

Step1: Start with Fiona's equation

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

Step2: Eliminate fractions, multiply by 5

$5y = 2x - 25$

Step3: Rearrange terms to match options

$2x - 5y = 25$

Step4: Scale equation (divide by 2)

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

Answer:

$\boldsymbol{x - \frac{5}{2}y = \frac{25}{2}}$ (the fourth option)