Answer :

iGreen
-6y + 2x = 18

Subtract 2x to both sides:

-6y = -2x + 18

Divide -6 to both sides:

y = -2/-6x - 3

Simplify:

y = 1/3x - 3

Now it's in the form of y = mx + b, where 'm' is the slope.

So the slope here is 1/3.
SchwarzschildRadius
First of all, I would like to thank Cosmos for deleting my incorrect answer. (applause)

Now, we will proceed to our main program.

Manipulate -6y + 2x = 18 into the y = mx + b form.

Subtract 2x from both sides
-6y = -2x + 18

Divide both sides by -6
[tex]y = \frac{-2}{-6}x + \frac{18}{-6} [/tex]

Simplify
[tex]y = \frac{1}{3} x - 3[/tex]

The slope will be the coefficient of x.

[tex]The\ slope\ is\ \frac{1}{3} \ .[/tex]