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.

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.

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.**

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.

Similar

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.