Section 1.5

Writing Equations of Parallel and Perpendicular Lines

Parallel lines – Two lines that are in the same plane and have no points in common. They have the same slope.

Coincide – Two lines that represent the same line.

Perpendicular lines – Two nonvertical lines in a plane with slopes that are opposite reciprocals.

Determine whether the graphs of each pair of equations are parallel,

perpendicular or neither.

The lines coincide.

Determine whether the graphs are parallel, coinciding, perpendicular, or neither.

2x+4y=4 x+2y=5

2x+4y=4 x+2y=54y=-2x+4 2y=-x+5y=-½ x+1 y=-½ x +5/2

The lines have the same slope but different y-intercepts. Therefore the lines are parallel.

y=-½ x+1 y=-½ x +5/2

5x-3y=1210x-6y=24

5x-3y=12 10x-6y=24 -3y=-5x+12 -6y=-10x+24 y= 5/3 x – 4 y=5/3 x -4

The lines have the same slope and intercept so they coincide.

y=2/3 x-63x+2y=9

perpendicular

2x-7y=14y=3x-7

neither

Write the standard form of the equation of the line that passes through the point (-2,10) and is

parallel to the graph of 2x+5y+4=0

Write the standard form of the equation of the line that passes through the point at (2,-3) and is

perpendicular to the graph of 6x-8y-5=0