Question

How do you write an equation in standard form given point (-2,4) and slope -3/2?

Answer 1

`3x+2y=2`

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.

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

`"here " m=-3/2" and " (x_1,y_1)=(-2,4)`

`rArry-4=-3/2(x+2)larrcolor(red)" in point-slope form"`

`"rearrange terms into standard form"`

`y-4=-3/2x-3`

`rArr3/2x+y=1larr" multiply through by 2"`

`rArr3x+2y=2larrcolor(red)" in standard form"`