Question

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

Answer 1

`2x+3y=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"`

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"to calculate m use the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(3,0)" and "(x_2,y_2)=(0,2)`

`rArrm=(2-0)/(0-3)=-2/3`

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

`"multiply through by 3"`

`rArr3y=-2x+6`

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