Question

What is the slope of 3x+6y+12=0​

Answer 1

Answer:

slope = - $\frac{1}{2}$

Step-by-step 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 = - $\frac{1}{2}$ x - 2 ← in slope- intercept form

with slope m = - $\frac{1}{2}$

Answer 2

Answer:

$\large\boxed{m=-\dfrac{1}{2}}$

Step-by-step 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)

$y=\dfrac{3}{-6}x+\dfrac{12}{-6}$

$y=-\dfrac{1}{2}x-2$

Therefore the slope

$m=-\dfrac{1}{2}$

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:

$m=\dfrac{-A}{B}$

We have

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

Substitute:

$m=\dfrac{-3}{6}=-\dfrac{1}{2}$