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: <span>3x + 6y = 12</span> ; Subtract "3x" from EACH side of the equation: __________________________________________________ 3x + 6y − 3x = 12 <span>− 3x ; </span> to get: 6y = 12 − 3x ; ↔ Rewrite as: 6y = -3x +12 ; <span>__________________________________________ 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" ; _________________________________________________________ </span>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) .
