Find an equation of the line. write the equation in function notation. through (6,-1); perpendicular to 9y=x-18

The first step is to find the slope of the given line by putting its equation in the form y = mx + b.
9y = x - 18
Dividing both sides by 9, gives:
y = (x/9) - 2
The slope of the given line is therefore 1/9.
Let the slope of the perpendicular line be m.
The product of the two slopes must equal -1 for the lines to be perpendicular.

Therefore m = -9.
At this stage the equation of the required line is y = -9x + b.
Now we need to find the value of b.
Plugging the given values of a point on the line (6, -1) into the equation gives:
-1 = -54 + b; from which b = 53.
The required equation for the line is:
f(x) = -9x + 53.