fionas equation\nfiona wrote the linear equation y = \\frac{2}{5}x - 5. when henry wrote his equation, they…

fionas equation\nfiona 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 fionas. which equation could be henrys?\n○ x - \\frac{5}{4}y = \\frac{25}{4}\n○ x - \\frac{5}{2}y = \\frac{25}{4}\n○ x - \\frac{5}{4}y = \\frac{25}{2}\n○ x - \\frac{5}{2}y = \\frac{25}{2}

fionas equation\nfiona 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 fionas. which equation could be henrys?\n○ x - \\frac{5}{4}y = \\frac{25}{4}\n○ x - \\frac{5}{2}y = \\frac{25}{4}\n○ x - \\frac{5}{4}y = \\frac{25}{2}\n○ x - \\frac{5}{2}y = \\frac{25}{2}

Answer

Explanation:

Step1: Rearrange Fiona's equation

Starting with $y = \frac{2}{5}x - 5$, we want to get it in the form $Ax+By = C$. First, subtract $\frac{2}{5}x$ from both sides: $-\frac{2}{5}x + y=- 5$. Then multiply through by - 5 to clear the fraction: $2x-5y = 25$. Now, we can also rewrite it in the form $x-\frac{5}{2}y=\frac{25}{2}$ by dividing the entire equation $2x - 5y=25$ by 2.

Answer:

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