# How do you write the equation y-6=1.3(x+7) in standard form?

Mar 12, 2017

$13 x - 10 y = - 151$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{standard form}}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y = C} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where A is a positive integer and B, C are integers.

distribute the bracket and rearrange into this form.

$y - 6 = 1.3 x + 9.1$

$\Rightarrow y = 1.3 x + 15.1$

We now require to multiply through by 10 as we require the coefficients to be integers.

$\Rightarrow 10 y = 13 x + 151$

subtract 10y from both sides.

$0 = 13 x - 10 y + 151$

subtract 151 from both sides.

$- 151 = 13 x - 10 y$

$\Rightarrow 13 x - 10 y = - 151 \leftarrow \textcolor{red}{\text{ in standard form}}$