Question

Write each equation in standard form.

$y-5=-2\left(x-3\right)$

Short answer

The equation in standard form is$\mathit{y}\mathbf{+}\mathbf{2}\mathit{x}\mathbf{=}\mathbf{11}$.

Step-by-step solution

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

A 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 $y-5=-2\left(x-3\right)$, apply the distributive property on the right side.

$$\begin{gathered} y-5=-2\left(x-3\right) \\ y-5=-2x-\left(-2\right)\times 3 \\ y-5=-2x+6 \end{gathered}$$

Step 3. Write the equation in standard form.

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

$$\begin{gathered} y-5=-2x+6 \\ y-5+5=-2x+6+5\text{Add5toeachside} \\ y+2x=-2x+11+2x\text{Add}2x\text{toeachside} \\ y+2x=11 \end{gathered}$$

Thus, the equation in standard form is $y+2x=11$.