Answer:
The question is written kinda bad, so i take the next two assumptions:
The original line is:
y = 5*x + 23
And we want to find a perpendicular line that passes through the point (-40, 2012)
Suppose that we have a linear equation:
y = a*x + b
A perpendicular line to this one, will have a slope equal to -(1/a)
Then a random perpendicular line to the one above, is:
y = -(1/a)*x + c
In this case, we start with the line:
y = 5*x + 23
Then the family of perpendicular lines to this one, will be like:
y = (-1/5)*x + c
Where c can be any real number.
Now, we also want this line to pass through (-40, 2012)
This means that when x = -40, the value of y must be 2012
We could replace these values in our equation above and solve it for c.
2012 = -(1/5)*(-40) + c
2012 = 40/5 + c
2012 = 8 + c
2012 - 8 = c = 2004
Then the equation is:
y = -(1/5)*x + 2004.
