Question

fiona wrote the linear equation y = 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?

Answer 1

From my research, the original equation Fiona wrote was "y = (2/5)x - 5". It also had choices as written below:

x – 5/4y = 25/4 

x –5/2 y = 25/4 

x –5/4 y = 25/2 

x –5/2 y = 25/2 

To obtain the possible equation Henry had written, the coefficient of x was removed, and the equation was placed in the form x + y = c. This is shown as follows:

y = (2/5) x – 5
[ y = (2/5) x – 5 ] (5/2)
(5/2)y = x - 25/2
 x - (5/2)y = 25/2 

Therefore, Henry's equation is x  – (5/2) y = 25/2.

Answer 2

Answer:

Henry's Equation is

$k.y=k.x-k.5\\where\: k\: can\: be\: any\: integer$

Step-by-step explanation:

Given: fiona's equation is y = x - 5 and Solution of fiona's equation and henry's equation are same.

To find: henry's equation

Two equation's have same solutions if one of the equation is multiple of other equation. ex,

y = x - 1 and 6y = 6x -6 or $\frac{2}{5}y=\frac{2}{5}x-\frac{2}{5}$

Therefore, their are many posible equations of Henry. For general say Henry's Equation is

$k.y=k.x-k.5\\where\: k\: can\: be\: any\: integer$