Kaitlyn -- here you go . . you need to put it in slope intercept form which is y = mx + b. You need to solve for y to have everything fall into place.
6x - 3y = 12
-6x -6x --> subtract 6x to move it away from the y
-3y = 12 - 6x --> u can rearrange if you would like
-3y = -6x + 12 --> remember to take the signs with the #'s when you rearrange!
/-3 /-3 /-3 --> divide everything by -3 to get y alone
y = 2x -4 --> in slope intercept form!
For an added bonus . . the slope would be 2 and the y-intercept -4!
For slope intercept form, you need to get it into the form of y=mx+b. For example, if you have 8x-2y=20 you would need to isolate the y. I like to work with positive numbers so I would add 2y to both sides. This would give you 8x=20+2y. Then I would move the 20 to the other side by subtracting it. This leaves you with 8x-20=2y. Finally, you divide both sides by 2 to get the y all by itself. This leaves you with 4x-10=y which is the slope intercept of my example.
If you don't want to move so many numbers, you can start by subtracting 8x from both sides to get the y on its own side right away. This would give you the equation -2y=-8x+20. Then you would divide by -2 to isolate the y. This gives you the final equation of y=4x-10. Either way, you get the same answer. Just don't forget, if you divide by a negative number, you need to switch the signs.
Slope intercept form is given by:
y = mx + b
where m is the slope and b is the y -intercept.
What you have is standard form:
Ax + By = C
To get into slope-intercept, solve for y:
Divide out by the common factor 3:
2x - y = 4
Rearrange for y:
y = 2x - 4
By slope-intercept form:
therefore, acc to the equation-
=> y= -6x/-3 + 12/-3
=> y= 2x-4
Hence, slope of the line = 2
& y-intercept= -4
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 .
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.