Question

How do you write the equation `y=2/3x+1` in standard form and identify A, B, C?

Answer 1

`2x-3y=-3`

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.

`"rearrange "y=2/3x+1" into this form"`

`"multiply through by 3 to eliminate the fraction"`

`rArr3y=2x+3`

`"subtract 3y from both sides"`

`cancel(3y)cancel(-3y)=2x-3y+3`

`rArr0=2x-3y+3`

`"subtract 3 from both sides"`

`0-3=2x-3ycancel(+3)cancel(-3)`

`rArr2x-3y=-3larrcolor(red)" in standard form"`

`rArrA=2, B=-3" and "C=-3`