To find the equation of the line parallel to the x-axis and passing through the point (-1, 9), we understand that the slope of any parallel-to-x-axis line is zero. This is because, on a line like this, the value of y remains fixed and does not rise or decline no matter what value x takes--a zero 'rise over run' scenario. So, this gives it the characteristic of the zero slope.
The general equation for a line in the slope-intercept form is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Since we know that our line is parallel to the x-axis, our 'm' (slope) will be zero. Substituting this into the equation makes it: y = 0*x + b, or simply y = b.
Now, this line will intersect the y-axis at the point where x is zero. But that doesn't help us as we are told that the line passes through the point (-1, 9). Therefore, we'll need to calculate the y-coordinate for the equation of our line by plugging in these values into the equation. So, we have:
9 = 0*-1 + b.
Solving for b, we find that b = 9.
Therefore, the equation of the line is y = 9.