# How do you write y+7=-3/2(x+1) in standard form?

Aug 28, 2017

See a solution process below:

#### 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

Therefore, we can first multiply each side of the equation by $\textcolor{red}{2}$ to eliminate the fractions so all of the coefficients and the constants are integers:

$\textcolor{red}{2} \left(y + 7\right) = \textcolor{red}{2} \times - \frac{3}{2} \left(x + 1\right)$

$2 \left(y + 7\right) = \cancel{\textcolor{red}{2}} \times - \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} \left(x + 1\right)$

$2 \left(y + 7\right) = - 3 \left(x + 1\right)$

Next, we can expand the terms on each side of the equation:

$\left(2 \times y\right) + \left(2 \times 7\right) = \left(- 3 \times x\right) + \left(- 3 \times 1\right)$

$2 y + 14 = - 3 x - 3$

Now, we can subtract $\textcolor{red}{14}$ and add $\textcolor{b l u e}{3 x}$ to each side of the equation to convert it to Standard Linear form:

$\textcolor{b l u e}{3 x} + 2 y + 14 - \textcolor{red}{14} = \textcolor{b l u e}{3 x} - 3 x - 3 - \textcolor{red}{14}$

$3 x + 2 y + 0 = 0 - 17$

$\textcolor{red}{3} x + \textcolor{b l u e}{2} y = \textcolor{g r e e n}{- 17}$