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

Jul 9, 2015

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

Explanation:

The (normally accepted) definition of standard form for a linear equation is:
$\textcolor{w h i t e}{\text{XXXX}}$$A x + B y = C$ with $A , b , C \epsilon \mathbb{Z}$ and $A \ge 0$
$\textcolor{w h i t e}{\text{XXXX}}$(occasionally you may see an added restriction that the $\gcd \left(A , B , C\right) = 1$ which I have supplied a second answer; check with your instructor).

Given $y = - 0.4 x + 1.2$

Convert everything to integers (elements of $\mathbb{Z}$) by multiplying all terms on both sides by 10
$\textcolor{w h i t e}{\text{XXXX}}$$10 y = - 4 x + 12$

Add $\left(4 x\right)$ to both sides to get "standard form"
$\textcolor{w h i t e}{\text{XXXX}}$$4 x + 10 y = 12$

(Divide all terms by $2$ to reduce so $\gcd = 1$)
$\textcolor{w h i t e}{\text{XXXX}}$$2 x + 5 y = 6$