##y = -2x – 13##
Perpendicular lines ##L## and ##L’## with slopes ##m## and ##m’##, respectively, have the following property with the slopes
##m = -1/m##
In case the is 0, the slope of the perpendicular line would be undefined, and vice versa. This would mean you are dealing with horizontal/vertical lines.
Given the line ##L: y = 1/2x + 5##, we have
##m = 1/2##
Which means the line ##L’## which is perpendicular to ##L## has the following slope
##m’ = -1/(1/2)##
##=> m’ = -2##
Now that we know the slope of ##L’##, let’s find its y-intercept.
##L’: y = -2x + b##
To find the y-intercept, let’s insert the point which we know lies on the line ##L’##.
##p’: (-9, 5)##
##=> L’: 5 = -2(-9) + b##
##=> -13 = b##
Therefore, the equation of the line ##L’## which is perpendicular to ##L## and passes through the point ##(-9, 5)## is
##y = -2x – 13##
