Q17. - Algebra 1

Question

Write each equation in standard form.

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

Step-by-Step Solution

Answer

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

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 $Ax+By=C$.

 $$\begin{gathered} y-5=-2x+6 \\ y-5+5=-2x+6+5\text{ Add 5 to each side} \\ y+2x=-2x+11+2x\text{ Add }2x\text{ to each side} \\ y+2x=11 \end{gathered}$$ 

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