Find the slope of the line described by x - 3y = - 6.

In slope-intercept form which is y=mx+b

where m=slope

b=y-intercept

so get into slope intercept form

x-3y=-6

add 3y to both sides

x=3y-6

add 6 to both sides

x+6=3y

divide both sides by 3

1/3x+2=y or

y=1/3x+2

y=mx+b

m=slope

slope=1/3

Y = mx + b

That is your goal

x - 3y = - 6

So first, subtract the x over to the other side

-3y = - x - 6

Then divide the whole equation by - 3

y = 1/3x + 2

This is now in the format of y = mx + b

m: slope

B: y-intercept

m/slope: 1/3