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what are the slope, m, and y-intercept, (0,b), of the line described by the equation 3x+6y=12? ?

The equation, in slope-intercept form; that is, "y = mx + b" ;   is:

                     y = (-1/2)x + 2 ;


The slope, "m" = -(1/2)  

The y-intercept, "b" = 2 ; that is, "(0, 2)" .

Explanation:

Given the linear equation: " 3x + 6y = 12 ";  which is written in "standard form"; that is:  "Ax + By = C" ;  

Rewrite the equation in "slope-intercept format";  or:  " y = mx + b " ;
    in which "y" is isolated as a "single variable" on the "left hand side";  
                 "m" is the coefficient of "x" ; and "m" = the slope of the line;  and
                 "b" is the "y-intercept" of the graph;  
               (that is, the coordinates of the "y-intercept of the graph are:  "(0, b)" .
Given:  3x + 6y = 12   ; Subtract "3x" from EACH side of the equation:

    3x + 6y − 3x = 12 − 3x ;  

to get: 6y = 12 − 3x ; ↔ Rewrite as:  6y = -3x +12 ;

Now, divide EACH side of the equation by "6"; to isolate "y" on the "left-hand side" of the equation; and to rewrite the equation in "slope-intercept format" ;

6y / 6 = [-3x +12] / 6 ;

to get:

y = (-3/6)x + (12/6) ;  

↔ y = (-1/2)x +2
 
The slope, "m", is -(1/2);  The y-intercept is "2";  (0,2) .