Question

How do you write the standard form of a line given x intercept = 3, y intercept = 2?

Answer 1

`2x+3y-6=0`

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=0)color(white)(2/2)|)))`
where A is a positive integer and B, C are integers.

`"express the equation in "color(blue)"slope-intercept form"`

`• y=mx+b " where m represents the slope and b, the"`
`color(white)(xxxxxxxxxxx)"y-intercept"`

`"here " b=2" and m=-2/3`

`rArry=-2/3x+2larrcolor(red)" in slope-intercept form"`

`"add " 2/3x" to both sides"`

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

`rArr2/3x+y=2`

`"subtract 2 from both sides"`

`2/3x+y-2=0`

`"multiply ALL terms by 3"`

`rArr2x+3y-6=0larrcolor(red)" in standard form"`