The equation, in slope-intercept form; that is, "y = mx + b" ; is:
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y = (-1/2)x + 2 ;
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The slope, "m" = -(1/2)
The y-intercept, "b" = 2 ; that is, "(0, 2)" .
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Explanation:
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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:
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3x + 6y − 3x = 12 − 3x ;
to get: 6y = 12 − 3x ; ↔ Rewrite as: 6y = -3x +12 ;
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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" ;
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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) .
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