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#?

1 Answer
Dec 25, 2016

Answer:

#y = -2x - 13#

Explanation:

Perpendicular lines #L# and #L'# with slopes #m# and #m'#, respectively, have the following property with the slopes

#m = -1/m#

In case the slope 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#