The line goes through (-9, -9) and is parallel to -x + 9y = 45.

First we will find the slope of the line -x + 9y = 45.

-x + 9y = 45

solving for y we get

y = 5 + (1/9)x

The slope is k = 1/9.

Now we need to find equation of a line with slope k = 1/9 going through (-9, -9).

y = (1/9)x + b, where b is y intercept

Plug (-9. -9) into the equation y = (1/9)x + b:

(1/9)*(-9) + b = - 9

-1 + b = - 9

b = -9 + 1

b = -8

The slope-intercept form of the line is:

y = (1/9)x - 8