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

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Answer 1 · 2016-06-06T19:10:35

$y= 4/5x-16/5$

Using first principles ( from which are derived the shortcuts)

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

Add $color(blue)(4x)$ to both sides. This turns the $-4x$ on the left into 0 and you end up with it on the right of = but being positive.

$color(brown)(-4xcolor(blue)(+4x)+5y+16= 0 color(blue)(+4x))$

$0+5y+16=4x$

Subtract $color(blue)(16)$ from both sides

$color(brown)(5y+16color(blue)(-16)=4xcolor(blue)(-16))$

$5y+0=4x-16$

Divide both sides by $color(blue)(5)$ . This turns the 5 from $5y$ into 1 as $5/5=1" and " 1xxy=y$

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

$y= 4/5x-16/5$

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