To find the equation of a line that is parallel to the line given by the equation \( y = x - 9 \) and passes through the point \((-8, -18)\), we first need to determine the slope of the given line.
The equation \( y = x - 9 \) can be rewritten in slope-intercept form, which is \( y = mx + b \). Here, the slope \( m \) is 1 (since the coefficient of \( x \) is 1).
Since parallel lines have the same slope, the line we want to find will also have a slope of 1.
Now we can use the point-slope form of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
where \( m \) is the slope, and \((x_1, y_1)\) is a point on the line. Substituting the slope and the coordinates of the given point \((-8, -18)\):
\[ y - (-18) = 1(x - (-8)) \]
This simplifies to:
\[ y + 18 = 1(x + 8) \]
Now, distribute the right side:
\[ y + 18 = x + 8 \]
Next, isolate \( y \):
\[ y = x + 8 - 18 \] \[ y = x - 10 \]
So, the equation of the line that is parallel to \( y = x - 9 \) and passes through the point \((-8, -18)\) is:
\[ \boxed{y = x - 10} \]