Write an equation of a line that is perpendicular to the line y = 2/3x + 5.

Solution:

The equation given in the problem statement is written in the slope and intercept form and hence the slope of the given equation y = (2/3)x + 5 is given as

m₁ = 2/3

It is known that if m₂ is the slope of the line perpendicular to the line of slope m₁ then

m₁ × m₂ = -1

If m₁ = 2/3 then

(2/3) × m₂ = -1

m₂ = - 3/2

Therefore the equation of the line perpendicular to y = (2/3)x + 5 is

y = (-3/2)x + c

Since the above equation can be perpendicular to y = (2/3)x + 5 at any given point the general equation the line is y = (-3/2)x + c

Write an equation of a line that is perpendicular to the line y = 2/3x + 5.

Summary:

The equation of a line that is perpendicular to the line y = 2/3x + 5 is y = (-3/2)x + c