To find the equation of a line that is parallel to the given line \( y = x - 9 \) and passes through the point \( (-8, -18) \), we first identify the slope of the given line.
The given line is in slope-intercept form \( y = mx + b \), where \( m \) represents the slope. The slope of the line \( y = x - 9 \) is 1 (since the coefficient of \( x \) is 1).
Since parallel lines have the same slope, the slope of the new line will also be 1.
Next, we will use point-slope form to find the equation of the line that passes through the point \( (-8, -18) \):
The point-slope form of a line is given by:
\[ y - y_1 = m(x - x_1) \]
Where \( (x_1, y_1) \) is the point the line passes through and \( m \) is the slope.
Substituting in our values:
- \( m = 1 \)
- \( x_1 = -8 \)
- \( y_1 = -18 \)
The equation becomes:
\[ y - (-18) = 1(x - (-8)) \]
This simplifies to:
\[ y + 18 = 1(x + 8) \]
Now distribute and simplify:
\[ y + 18 = x + 8 \]
Subtract 18 from both sides:
\[ y = x + 8 - 18 \]
\[ y = x - 10 \]
The final equation for the line parallel to \( y = x - 9 \) and passing through the point \( (-8, -18) \) is:
\[ \boxed{y = x - 10} \]