Question

show that lines 3x+2y=5 and 2x-3y=6 are perpendicular​

Answer 1

Thus the lines 3x+2y =5 and 2x-3y=6 are perpendicular.

• To know whether the lines are perpendicular we need to check the slopes of the lines.
• If the product of the slopes of lines is equal to -1 then the lines are perpendicular.
• Now the given lines are 3x+2y =5 and 2x-3y=6.
• Converting the given lines in the form y=mx+c , where m is the slope of the line and c is the y-intercept.
• The first equation becomes y = (-3/2)x +(5/2)
• Slope of the line(m₁) is -3/2.
• The second equation becomes y = (2/3)x -2
• Slope of the line is (m₂) is 2/3.
• Product of the slopes is m₁m₂.

m₁m₂ = (-3/2)(2/3)

m₁m₂ = -1

• Therefore the lines are perpendicular.