6x-3y=12 is the equation of straight line on a Catesian Plane, as it is a linear equation of two variables x and y. The slope and intercept form of an equation of a line in a plane is given by y=mx+c, where m is the slope and c is the y intercept, on y axis.
Any equation can be transformed by simple operations like: adding equals on both sides of the equation,subtracting equals from both sides of the equation , multiplying or dividing by equals(but other than zero) both sides of the equation, without affecting the solution of the equation.
So we multiply the given equation by (-1) :
(-1)(6x)-(-1)(3y)=(-1)(12) and simplify.
-6x+3y=-12. Divide by 3
-2x+y=-4. Add 2x .
-2x+2x+y=2x-4. Simplify.
y=2x-4. which is in the standard slope intercept form like,y=mx+c=0. Now comparing the coeffcients of y,x and constant terms in these two equations we get:
1/1=2/m=-4/c equations in (1).
Therefore,bythe equality of first two terms in equation flagged at (1), 1=2/m, we get, m=1/2 .
From the equation (equating first and last terms) in(1) , we get:1=-4/c or c=4.
Threfore the slope of the given rquation is 2 and the straight line intercepts the y axis at -2 or 2 units below the origin.
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