Question

How do you write `y= -0.4x + 1.2` in standard form?

Answer 1

`4x+10y = 12`
or
`2x+5 = 6`

Explanation:

The (normally accepted) definition of standard form for a linear equation is:
`color(white)("XXXX")` `Ax+By=C` with `A, b, C epsilon ZZ` and `A>=0`
`color(white)("XXXX")`(occasionally you may see an added restriction that the `gcd(A,B,C) = 1` which I have supplied a second answer; check with your instructor).

Given `y = -0.4x +1.2`

Convert everything to integers (elements of `ZZ`) by multiplying all terms on both sides by 10
`color(white)("XXXX")` `10y = -4x+12`

Add `(4x)` to both sides to get "standard form"
`color(white)("XXXX")` `4x+10y = 12`

(Divide all terms by `2` to reduce so `gcd=1`)
`color(white)("XXXX")` `2x+5y=6`