Answer: y = (1/3)*x - 7
Explanation:
When we have a line:
y = a*x + b
A perpendicular line to this one needs to have a slope s equal to:
s = -(1/a)
Then any line written as:
y = -(1/a)*x + c
is perpendicular to the lines of the form "y = a*x + b"
Then if we have the line:
y = -3*x - 8
The family of perpendicular lines to this one is:
y = -(1/-3)*x + c
y = (1/3)*x + c
where c can be any real number.
Now we also want that this line passes through the point (9, -4)
Then we need to replace x by 9, and y by -4
-4 = (1/3)*9 + c
Now we can solve this for c.
-4 = 9/3 + c
-4 = 3 + c
-4 - 3 = c
-7 = c
Then the line that is perpendicular to the line y = -3x – 8 and that goes through (9, -4) is:
y = (1/3)*x - 7