Which pair of equations are perpendicular lines?

Question

B.x – 3y = 11 and y = –3x + 23

C.4x + 2y = 6 and y = –2x + 18

D.x – 3y = 5 and y = 3x – 11

Answer 1

If the slopes are negative reciprocal to each other, then the lines are perpendicular.

Write the each line equation in slope-intercept form y = mx+b, where m = slope and b = y-intercept.

 

B) The two line equations are x - 3y = 11 and y = - 3x + 23.

x - 3y = 11 ⇒ y = (1/3)x - 11/3.

Slope of the first line m₁ = 1/3.

Slope of the second line m₂ = - 3.

The two slopes are negative reciprocal to each other, so the pair of equations are perpendicular lines.

 

C) The two line equations are 4x + 2y = 6 and y = - 2x + 18.

4x + 2y = 6 ⇒ y = - 2x + 3.

Slope of the first line m₁ = - 2.

Slope of the second line m₂ = - 2.

The two slopes are not negative reciprocal to each other, so the pair of equations are not perpendicular lines.

 

D) The two line equations are x - 3y = 5 and y = 3x - 11.

x - 3y = 51 ⇒ y = (1/3)x - 5/3.

Slope of the first line m₁ = 1/3.

Slope of the second line m₂ = 3.

The two slopes are not negative reciprocal to each other, so the pair of equations are not perpendicular lines.