Answer:
slope = - [tex]\frac{1}{2}[/tex]
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 = - [tex]\frac{1}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Answer:
[tex]\large\boxed{m=-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation in general form
[tex]Ax+By+C=0[/tex]
Convert it to the slope-intercept form:
[tex]3x+6y+12=0[/tex] subtract 6y from both sides
[tex]3x+12=-6y[/tex] divide both sides by (-6)
[tex]y=\dfrac{3}{-6}x+\dfrac{12}{-6}[/tex]
[tex]y=-\dfrac{1}{2}x-2[/tex]
Therefore the slope
[tex]m=-\dfrac{1}{2}[/tex]
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:
[tex]m=\dfrac{-A}{B}[/tex]
We have
[tex]3x+6y+12=0\to A=3,\ B=6[/tex]
Substitute:
[tex]m=\dfrac{-3}{6}=-\dfrac{1}{2}[/tex]
