# Parallel, Perpendicular, Coinciding, or Intersecting Lines ```Parallel, Perpendicular, Coinciding, or Intersecting
Lines
To determine if the graphs of two equations are lines that are parallel,
perpendicular, coinciding, or intersecting (but not perpendicular), put the
equations in slope-intercept form (solve each equation for y). Then by looking at
the equation you will be able to determine what type of lines they are.
Slope-intercept Form
y = mx + b
m &AElig; slope
b &AElig; y-intercept
Parallel Lines
lie in same plane and never intersect
have same slope
equations have same x-coefficient
1
y = − x −1
2
1
y = − x +2
2
Perpendicular Lines
lie in same plane and intersect at 90o angle
slopes are negative reciprocals
y = 2x − 1
m1 = 2
1
y = − x +2
2
m2 = −
1
2
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Coinciding Lines
lie right on top of each other
same slope
same y-intercept
1
y = − x+2
2
1
y = − x+2
2
Intersect at one point
Different slopes
Not perpendicular
Intersecting Lines
1
y = − x+2
2
y = x −3
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