# What is the equation in standard form of the line with slope m=-1/3 and intercept b=-6?

mathsworkmusic | (Level 2) Educator

Posted on

The slope-intercept form of a linear equation is

`y = mx + b`

The standard form is

`Ax + By + C = 0`

where ` ``A >= 0`. Also, to simplify the equation, we require `A,B,C` to be integer.

We are given that `m = -1/3`  and `b = -6`

so in slope-intercept form the equation is

`y = -1/3x - 6`.

Rearranging this equation by bringing all terms over to the lefthand side, we get

` ``1/3x + y +6 = 0`` `.

To simplify, we multiply both sides by 3 (to get rid of the fraction) to get

`x + 3y + 18 = 0`

In standard form then, the equation of the line is

`Ax + By + C = 0`

where `A = 1, B=3,C=18`

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

b=-6 ,y intercept  (if)  , m=-1/3

let x intercept is a

`x/a+y/b=1`

`y/b=-x/a+1`

`y=(-b/a)x+b`

`which`  si similar to

`y=mx+c`

given

-b/a=-1/3

`6/a=-1/3`

`a=-18`

Thus equation reduces to

`x/(-18)+y/(-6)=1`

`x+3y+18=0`