What is the slope of the line whose equation is -x+3y=2

Just rearrange in terms of y, and the x coefficient is your slope:

-x + 3y = 2
y = (x + 2)/3
m = 1/3

To determine the slope, you need to put the equation into y = mx + b form.

-x + 3y = 2
3y = x + 2
y = 1/3x + 2/3

Whatever is in front of x in this form is the slops, so you can see that the slope is m = 1/3.

-x+3y=2
3y=x+2
divide by 3

y=x/3 + 2/3

It's now in the form y=mx+b where m = slope. m = 1/3

-x+3y=2

3 y = x+2

y = 1/3 x + 2/3

since line equation is
y = mx+c where

m = slope.

hence

slope of the line given by -x+3y=2 is = 1/3

the slope is -1/3 :)

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-1/2 negative one over two

1/3

Slope in Ax+By=C is always -(a/b)

1/3