Write the equation of the line that passes through P and is perpendicular to the given line

Question

P(4,5)y=-1/3x-6

Answer 1

Data for the given equation is...

y=(-1/3)x-6
m₁= -1/3
y-intercept is (0,-6)
m₂=3.....slope of a perpendicular line to the given (negative
              reciprocal of "m₁")

For P=(4,5), substitute these values into the point-slope
form equation "y=mx₂+b" where "m₂=3".
5=3(4)+b....solve for "b"

 b=7

 

...and rewrite new perpendicular point-slope equation...

y=3x-7........new perpendicular line passing thru P(4,5)

 

Substitute point P(4,5) into this new equation to check 

for truth...

5=3(4)-7

5=12-7

5=5.........true, √check, new perpendicular line equation

                is correct.

 

Always check your solution and work.