# When given a question like: 6x-3y=12, then asked to put it in slope intercept form and solve I'm stumped. Can anyone help me?

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### 6 Answers

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:

6x-3y=12

Divide out by the common factor 3:

2x - y = 4

Rearrange for y:

y = 2x - 4

6x-3y=12

6x-3y-6x=12-6x

-3y=12-6x

-3y/-3=12/-3-6x/-3

y=-4+2x

y=2x-4

slope intercept=2

y-intercept=-4

By slope-intercept form:

y=mx+c

therefore, acc to the equation-

6x-3y=12

=> -3y=-6x+12

=> 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=**m**x+**c**, where **m **is the **slop**e 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.