Question

Write each equation in standard form.

$y+4=\frac{2}{3}\left(x-3\right)$

Short answer

The equation in standard form is$\mathbf{2}\mathit{x}\mathbf{-}\mathbf{3}\mathit{y}\mathbf{=}\mathbf{18}$.

Step-by-step solution

Step 1. State the concept of the standard form of an equation.

The standard form of a linear equation is$Ax+By=C$ where $A\ge 0$, $A$ and $B$ are not both zero, and $A,B$and $C$are integers with a greatest common factor of 1.

The slope-intercept form of a linear equation is $y=mx+b$, where $m$is the slope and $b$is the $y$-intercept.

Step 2. Simplify the equation. 

In order to simplify $y+4=\frac{2}{3}\left(x-3\right)$, first multiply both sides by 3 and then apply the distributive property.

$$\begin{gathered} 3\times \left(y+4\right)=3\times \frac{2}{3}\left(x-3\right) \\ 3\times \left(y+4\right)=2\times \left(x-3\right) \\ 3y+12=2x-6 \end{gathered}$$

Step 3. Write the equation in standard form.

Further, simplify the equation so as to rewrite the equation in the needed form of $Ax+By=C$.

$$\begin{gathered} 3y+12=2x-6 \\ 3y+12-12=2x-6-12\text{Subtract12fromeachside} \\ 3y-2x=2x-18-2x\text{Subtract}2x\text{fromeachside} \\ \left(-1\right)\times \left(3y-2x\right)=\left(-1\right)\times \left(-18\right)\text{Multiplybothsidesby-1} \\ 2x-3y=18 \end{gathered}$$

Thus, the equation in standard form is $2x-3y=18$.