Part 1: Coinciding Lines Parallel Lines
Coinciding Lines: Definition: Lines that have all solutions in common in an input/output table. They overlap Same slope, same y-intercept, same line…
Coinciding Lines Example xy Line A : y = -1x + 2 xy Line B: y = -1x + 2
Practice: Identifying Coinciding Lines Match the coinciding lines: y = 3x + 2 y = -1x – 2 y = -x + 4 y = x x + 6y = 18 2y = 6x x – 5y = -20 -y = 1x + 2
Parallel Lines: Definition: Lines that have no intersection No solutions the same in an input/output table same slope, different y-intercept (same line that crosses at a different point on the y-axis)
Parallel Lines Example xy Line A xy Line A : y = -1x + 2 Line B: y = -1x – 1 NOTICE: the slope is the same, but not the y-intercept
Practice: Identifying Parallel Lines Match the parallel lines: y = 3x + 2 y = -1x – 2 y = x + 4 y = x + 3 y = x + 5 y = x + 2 y = 3x – 7 y = -x
Practice: Writing Parallel Lines Write an equation of a line that is parallel to each of the following lines. y = 4x + 2 y = 3x – 2 y = -x + 4 y = x + 3
Part 2: Perpendicular Lines Intersecting Lines
Intersecting Lines: Definition: Lines that intersect or cross at one point Only one solution in common- at intersection Only one solution in common on an input/output table
Intersecting Lines Example xy xy Line ALine A : y = -1x + 2 Line B: y = x – 1 NOTICE: the only thing in common is the point or solution at which the input and output are the same
Perpendicular Lines: Definition: Lines that intersect at one point, creating four 90 degree angles. Only one solution in common- at intersection Opposite reciprocal slopes of each other Y-intercepts different *SPECIAL CASE: y-intercepts CAN be the same if they cross (intersect) on the y-axis
Perpendicular Lines Example xy xy Line ALine A : y = x + 2 Line B: y = +2x + 1 NOTICE: the slope is the opposite reciprocal (opposite sign and flip fraction of slope ) NOTICE: they have one point in common
Line B: y = +2x + 1 Perpendicular Lines SPECIAL CASE xy xy Line ALine A : y = x + 1 NOTICE: the slope is the opposite reciprocal (opposite sign and flip fraction of slope ) AND the y-intercept because they intersect at the y-axis NOTICE: they have one point in common + 1
How to Identify Perpendicular Lines: Slopes will have the opposite sign and reciprocal Example: y = 3x + 1 slope is 3 or A line PERPENDICULAR will have a slope of the opposite sign and reciprocal slope will be
Practice: Identifying Perpendicular Slopes Write a slope that is perpendicular to the slope in the equations given. y = 4x + 2 y = 3x – 2 y = -x + 4 y = x + 3
What about the Special Case? The only time that the y-intercepts match in perpendicular lines is when they intersect on the y-axis.