To solve this, you must put the equation in slope-intercept form, which is y=mx+b.
To do this, isolate y.
First, subtract 3x from both sides.
3x + 9y = -9
3x + 9y - 3x = 9y
-9 - 3x = -9 - 3x
9y = -9 - 3x
Now, divide both sides by 9.
9y = -9 - 3x
9y / 9 = y
-9 / 9 = -1
-3x / 9 = -0.33x = -1/3x
y = -1 - 1/3x
In y = mx + b form:
y = -1/3x - 1
In slope intercept form, m is the slope.
In our answer, -1/3 is m, so it is the slope.
So the final answer is that the slope is -1/3.
Hope this helps!
