Question

Write the given equation in standard form.

$\mathit{y}\mathbf{-}\mathbf{9}\mathbf{=}\mathbf{-}\frac{\mathbf{4}}{\mathbf{5}}\left(x+2\right)$

Short answer

The equation of the line in standard form is $\mathbf{4}\mathit{x}\mathbf{+}\mathbf{5}\mathit{y}\mathbf{=}\mathbf{37}$.

Step-by-step solution

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,

$\begin{array}{c}y-9=-\frac{4}{5}\left(x+2\right)\\ 5\left(y-9\right)=-4\left(x+2\right)\\ 5y-45=-4x-8\\ 5y+4x=-8+45\\ 4x+5y=37\end{array}$

This equation is in standard form $ax+by=c$, where$a=4,b=5$ and $c=37$.

Therefore, the equation of the line in standard form is $4x+5y=37$.