2y- x/3 = 12   what is the slope?

6 Answers

brianevery's profile pic

brianevery | High School Teacher | (Level 2) Adjunct Educator

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There are many ways to find the slope - the easiest being to put the equation into the slope intercept form, which is

y=mx+b where m represents the slope and b represents the y intercept

To do this, we want to solve the equation 2y-x/3=12 for y

first add x/3 to both sides of the equation to get

2y=12+x/3 or 2y=x/3+12

Our next step would be to divide both sides by 2 but this could be a bit messy with x already being divided by 3. We can eliminate the fraction x/3 by multiplying the entire equation by 3 before doing anything else - this would give us

3(2y=x/3+12) => 6y=x+36

Now if we divide everything by 6 we will isolate the y on the left side of the equation, and the coefficient of the x term will be our slope

y=x/6+6 or we can separate the x/6 and make it a multiplication like this (1/6)x so the equation now looks like this

y=(1/6)x+6 and by looking at the coefficient of x we see that our slope is 1/6.

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

2y-x/3 =12

To find the slope we need to rewrite the function with the standard form y=mx +b   where m is the slope

2y -x/3 =12

2y = x/3 +12

Divide by 2:

y= x/6 + 6

Then the slope would be x factor which is 1/6

User Comments

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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The slope of a line is the rate of change of y with respect to x. This is given by the derivative `dy/dx` .

To determine slope of the line `2y- x/3 = 12` taken the derivative with respect to x.

`(d(2y- x/3))/dx = (d12)/dx`

`2*dy/dx - (1/3) = 0`

`2*dy/dx = 1/3`

`dy/dx = 1/6`

The slope of the line 2y- x/3 = 12 is 1/6.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To find out the value of the slope, first we have to write that form of the equation of the line where slope is involved.

This form is:

y = mx + n, where m represents the slope

Now, we'll put the given equation into the form above, to emphasize the value of the slope.

2y- x/3 = 12

First step is to isolate y to the left side and to move all terms to the right side, with the changed sign.

2y = 12 + x/3

The next step is to divide both sides, by 2:

 y = 6 + x/6

Now, we'll evaluate:

y = mx + n  and  y = x/6 + 6

For these expressions to be identically, the correspondent coefficients have to be the same:

m = 1/6

n = 6

So, the slope is m = 1/6.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

2y-x/3 =12.To find the slope of the line.

The slope of the line is the expressed as the tangent of the angle made by the line with x axis.

The slope of the line ax+by +c = 0 is -a/b or (-coefficient of x)/(coefficient of y).

So the slope of the line 2y-x/3 = 0 Or (1/3)+2y-12 = 0 is =  -(-1/3)/3 = 1/9 . The line 2y-x/3 = 12 makes an angle A = arctan (1/9) = 6.34 degree nearly with x axis.


krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

The slope of a line represented by an equation in the form:

y = mx + c

is represented by the constant m in the equation.

To find the slope of given line we transform the equation of the line to the form y = mx +c as follows:

2y - x/3 = 12

2y = x/3 + 12

y = x/3/2 + 12/2

y = (1/6)x +6

Therefore slope of the line is 1/6.