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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msrobinsonlovesalgebra's profile pic

msrobinsonlovesalgebra | High School Teacher | (Level 1) Adjunct Educator

Posted on

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!

londieba's profile pic

londieba | Elementary School Teacher | eNotes Newbie

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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.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

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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

Jyotsana's profile pic

Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

Posted on

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

itssnigdha's profile pic

itssnigdha | Student, Grade 11 | (Level 2) Honors

Posted on

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

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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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