Question

A coordinate grid with a line labeled y equals StartFraction 2 over 5 EndFraction x minus 5 passing through the points (negative 5, negative 7) and (0, negative 5)
Fiona wrote the linear equation y = y equals StartFraction 2 over 5 EndFraction x minus 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?

x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 4 EndFraction.y =
x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 4 EndFraction.y =
x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 2 EndFraction.y =
x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 2 EndFraction.y =

Answer 1

x − (5/2)y = 25/2

Reason: Multiply both sides by 2 to get 2x − 5y = 25, which rearranges to y = (2/5)x − 5, the same line as Fiona’s.