To find the slope of the line represented by the equation 3x + 9y = 4, we need to rearrange it into the slope-intercept form, which is y = mx + b, where m represents the slope.
Starting with the given equation:
3x + 9y = 4
We can isolate y by first moving 3x to the other side:
9y = 4 - 3x
Next, divide everything by 9 to solve for y:
y = - rac{3}{9}x + rac{4}{9}
This simplifies to:
y = - rac{1}{3}x + rac{4}{9}
From this equation, we can see that the slope (m) of the line is -1/3.
Thus, the slope of the line 3x + 9y = 4 is -1/3.