Question

What is the slope of 3x+6y+12=0​

Answer 1

slope = -
`(1)/(2)`

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 6y + 12 = 0 into this form

Subtract 3x + 12 from both sides

6y = - 3x - 12 ( divide all terms by 6 )

y = -
`(1)/(2)` x - 2 ← in slope- intercept form

with slope m = -
`(1)/(2)`

Answer 2

`\large\boxed{m=-(1)/(2)}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

We have the equation in general form

`Ax+By+C=0`

Convert it to the slope-intercept form:

`3x+6y+12=0` subtract 6y from both sides

`3x+12=-6y` divide both sides by (-6)

`y=(3)/(-6)x+(12)/(-6)`

`y=-(1)/(2)x-2`

Therefore the slope

`m=-(1)/(2)`

Other method.

If we have the equation of lines in the general form Ax + By + C = 0 or the standard form Ax + By = C, then the slope is equal to:

`m=(-A)/(B)`

We have

`3x+6y+12=0\to A=3,\ B=6`

Substitute:

`m=(-3)/(6)=-(1)/(2)`