# How do you write y+2.1=1.4(x-5) in standard form?

Feb 11, 2017

$\textcolor{red}{14} x - \textcolor{b l u e}{10} y = \textcolor{g r e e n}{91}$

#### Explanation:

The standard form of a linear equation is: $\textcolor{red}{A} x + \textcolor{b l u e}{B} y = \textcolor{g r e e n}{C}$

where, if at all possible, $\textcolor{red}{A}$, $\textcolor{b l u e}{B}$, and $\textcolor{g r e e n}{C}$are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

To transform, first, multiply each term in parenthesis on the right side of the equation by $\textcolor{red}{1.4}$

$y + 2.1 = \left(\textcolor{red}{1.4} \times x\right) - \left(\textcolor{red}{1.4} \times 5\right)$

$y + 2.1 = 1.4 x - 7$

Next, subtract $\textcolor{red}{2.1}$ and $\textcolor{b l u e}{1.4 x}$ from each side of the equation:

$- \textcolor{b l u e}{1.4 x} + y + 2.1 - \textcolor{red}{2.1} = - \textcolor{b l u e}{1.4 x} + 1.4 x - 7 - \textcolor{red}{2.1}$

$- 1.4 x + y + 0 = 0 - 9.1$

$- 1.4 x + y = - 9.1$

Now, multiply each side of the equation by $\textcolor{red}{- 10}$ to complete the transformation:

$\textcolor{red}{- 10} \left(- 1.4 x + y\right) = \textcolor{red}{- 10} \times - 9.1$

$\left(\textcolor{red}{- 10} \times - 1.4 x\right) + \left(\textcolor{red}{- 10} \times y\right) = 91$

$14 x - 10 y = 91$