# How do you write y - 6 = 4(x + 3)  in standard form?

Jun 14, 2017

Polynomial standard form: $y = 4 x + 18$

#### Explanation:

Warning: standard form when not qualified and applied to a linear relation usually means $\textcolor{b l u e}{\text{linear standard form}}$ which is $A x + B y = C$ with $A , B , C \in \mathbb{Z} , \mathmr{and} A \ge 0$

However this question was asked under "Polynomials in Standard Form", so I have assumed you want something of the form:
$\textcolor{w h i t e}{\text{XXX")color(red)(y= "polynomial standard form expression}}$

A $\textcolor{red}{\text{polynomial standard form expression}}$ arranges the variable terms (typically with $x$ used as the variable) win descending sequence of exponents: $\textcolor{red}{{a}_{n} {x}^{n} + {a}_{n - 1} {x}^{n - 1} + \ldots + {a}_{2} {x}^{2} + {a}_{1} {x}^{1} + {a}_{0} {x}^{0}}$

Given
$\textcolor{w h i t e}{\text{XXX}} y - 6 = 4 \left(x + 3\right)$
we can expand the right side:
$\textcolor{w h i t e}{\text{XXX}} y - 6 = 4 x + 12$
then adding $6$ to both sides:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{red}{4 x + 18}$

It would be unusual, but you could write this to make the $\textcolor{red}{\text{polynomial standard form}}$ explicit:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{red}{4 \cdot {x}^{1} + 18 \cdot {x}^{0}}$

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Without going into the details of derivation, if you wanted the $\textcolor{b l u e}{\text{ linear standard form}}$ is would be
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{4 x - y = - 18}$