A line has the equation:
y = mx + c
where m = slope and c = y-intercept
This means we need to rearrange your equation a little to find out what the slope is.
3x + 9y - 7 = 0
We want to get the 'y' term on it's own. To do this we first can add 7 to both sides of the equation:
3x + 9y - 7 = 0
3x + 9y - 7 + 7 = 7
3x + 9y = 7
Now we can subtract 3x from both sides of the equation:
3x + 9y = 7
3x - 3x + 9y = - 3x + 7
9y = - 3x + 7
Now we can divide both sides of the equation by 9:
9y = - 3x + 7
(9y)/9 = (- 3x)/9 + 7/9
y = (- 3/9)x + 7/9
This means that using the equation of a line (which is y = mx + c)
m = - 3/9 = slope of the line
But since -3/9 can be simplified to become,
-3/9 = (-1x3)/(3x3) = - 1/3
The slope of the line is -1/3 