Question

How do you write `y = 1/2x – 3` in standard form?

Answer 1

`x-2y=6`

Explanation:

`"the equation of a line in "color(blue)"standard form "` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))`

`"where A is a positive integer and B, C are integers"`

`"multiply all terms in the equation by 2"`

`rArr2y=x-6`

`"subtract 2y from both sides"`

`cancel(2y)cancel(-2y)=x-2y-6`

`rArrx-2y-6=0`

`"add 6 to both sides"`

`x-2ycancel(-6)cancel(+6)=0+6`

`rArrx-2y=6larrcolor(red)"in standard form"`

Answer 2

`x-2y=6`

Explanation:

The standard form for a linear equation is:

`Ax+By=C`,

where if at all possible:

`A, B, and C` are integers, and `A` is non-negative, and `A, B, and C` have no common factors other than 1.
http://courses.wccnet.edu/~palay/precalc/22mt01.htm

`y=1/2x-3` is in slope-intercept form. To convert to standard form, subtract `1/2x` from both sides.

`-1/2x+y=-3`

Multiply both sides by `-2`.

`color(red)cancel(color(black)(-2))(-1/color(red)cancel(color(black)(2))x)+ -2(y)=-3xx-2`

Simplify.

`x-2y=6`