Q33. - Algebra 1

Question

Write the given equation in standard form.

$\mathit{y}\mathbf{+}\mathbf{4}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\left(x-3\right)$

Step-by-Step Solution

Answer

The equation of the line in standard form is $\mathit{x}\mathbf{-}\mathbf{2}\mathit{y}\mathbf{=}\mathbf{11}$.

Step 1. Standard form of the linear equation:

The standard form of an equation of a line is given by,

$ax+by=c$

Where, $a,b$ and, $c$ are the real numbers.

Step 2. Change the equation in standard form.

The equation is given by,

$\begin{array}{c}y+4=\frac{1}{2}\left(x-3\right)\\ 2\left(y+4\right)=1\left(x-3\right)\\ 2y+8=x-3\\ x-2y=8+3\\ x-2y=11\end{array}$

This equation is in standard form $ax+by=c$, where $a=1,b=-2$ and  $c=11$.

Therefore, the equation of the line in standard form is $x-2y=11$.