What is an equation of the line that passes through the point (-9,5) and is perpendicular to the line whose equation is ##y=1/2x+5##?

##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##