# How do you write -4x+5y+16=0 in standard form?

Jun 6, 2016

$y = \frac{4}{5} x - \frac{16}{5}$

Using first principles ( from which are derived the shortcuts)

#### Explanation:

To start off with $y$ being positive we have to leave it on the left of = and move everything else.

Add $\textcolor{b l u e}{4 x}$to both sides. This turns the $- 4 x$ on the left into 0 and you end up with it on the right of = but being positive.

$\textcolor{b r o w n}{- 4 x \textcolor{b l u e}{+ 4 x} + 5 y + 16 = 0 \textcolor{b l u e}{+ 4 x}}$

$0 + 5 y + 16 = 4 x$

Subtract $\textcolor{b l u e}{16}$ from both sides

$\textcolor{b r o w n}{5 y + 16 \textcolor{b l u e}{- 16} = 4 x \textcolor{b l u e}{- 16}}$

$5 y + 0 = 4 x - 16$

Divide both sides by $\textcolor{b l u e}{5}$. This turns the 5 from $5 y$ into 1 as $\frac{5}{5} = 1 \text{ and } 1 \times y = y$

color(brown)(5/(color(blue)(5))xxy=4/(color(blue)(5))x-16/(color(blue)(5))

$y = \frac{4}{5} x - \frac{16}{5}$