How do you write the equation y+3=3(x+5) in standard form?

Dec 27, 2017

The Standard Form of a Linear Equation is given by

$\textcolor{red}{A x + B y = C}$

Hence our Final Solution in Standard Form is

$\textcolor{b l u e}{- 3 x + y = 12}$

Explanation:

We are given the following equation:

$y + 3 = 3 \left(x + 5\right)$ Equation.1

Using Distributive Property we get,

$y + 3 = 3 x + 15$

Add $\textcolor{red}{\left(- 3\right)}$ to both sides to simplify:

$y \cancel{+ 3} + \textcolor{red}{\left(\cancel{- 3}\right)} = 3 x + 15 + \textcolor{red}{\left(- 3\right)}$

On simplification we get,

$y = 3 x + 15 + \textcolor{red}{- 3}$

$\Rightarrow y = 3 x + 12$ ... Equation.2

Note that we now have the equation in Slope-Intercept Form

Using basic algebraic concepts, we can obtain the equation in Standard Form

We want both the $x \mathmr{and} y$ terms on one side and the constant on the other side of our equation to write in Standard Firm

We will add $\textcolor{red}{\left(- 3 x\right)}$ to both sides of our Equation.2 to get

$y + \textcolor{red}{\left(- 3 x\right)} = 3 x + 12 + \textcolor{red}{\left(- 3 x\right)}$

$\Rightarrow y + \textcolor{red}{\left(- 3 x\right)} = \cancel{3 x} + 12 + \textcolor{red}{\cancel{- 3 x}}$

$\Rightarrow y - 3 x = 12$

Rewriting the equation to match $\textcolor{red}{A x + B y = C} ,$ which is the Standard Form we get

$\textcolor{b l u e}{- 3 x + y = 12}$

Hope this helps.

Dec 27, 2017

$3 x - y = - 12$

Explanation:

$\text{the equation of a line in "color(blue)"standard form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

$y + 3 = 3 x + 15$

$\text{rearrange into standard form}$

$\Rightarrow 3 x - y = - 12 \leftarrow \textcolor{red}{\text{in standard form}}$