Determine wether the graphs of y = -2/3x and 3x - 2y = 6 are perpendicular lines

Answer 1

Perpendicular Lines :

• If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular.

• If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.

The equations of two lines are y = - 2/3x and 3x - 2y = 6.

The equation 1 : y = - 2/3x is already adjusted in slope - intercept form or y = mx + b and its slope m₁ = - 2/3.

Write the equation 2 : 3x - 2y = 6 in slope intercept form or y = mx + b.

3x - 2y = 6

- 2y = - 3x + 6

y = (3/2)x - 3.

The slopes of two lines are m₁ = - 2/3 and m₂ = 3/2 and these are negative reciprocals.

Therefore, two lines y = - 2/3x and 3x - 2y = 6 are perpendiculars.