1. Part 1: Coinciding Lines Parallel Lines

2. Coinciding Lines: Definition: Lines that have all solutions in common in an input/output table. They overlap Same slope, same y-intercept, same line…

3. Coinciding Lines Example xy 3 11 20 Line A : y = -1x + 2 xy 3 11 20 Line B: y = -1x + 2

4. Practice: Identifying Coinciding Lines Match the coinciding lines: y = 3x + 2 y = -1x – 2 y = -x + 4 y = x + 3 -4x + 6y = 18 2y = 6x + 4 -5x – 5y = -20 -y = 1x + 2

5. 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)

6. Parallel Lines Example xy 3 11 20 Line A xy 0 1-2 2-3 Line A : y = -1x + 2 Line B: y = -1x – 1 NOTICE: the slope is the same, but not the y-intercept

7. 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

8. 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

9. Part 2: Perpendicular Lines Intersecting Lines

10. 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

11. Intersecting Lines Example xy 3 11 20 xy -44 11 30 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

12. 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

13. Perpendicular Lines Example xy 1-2 3-3 xy 01 24 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

14. Line B: y = +2x + 1 Perpendicular Lines SPECIAL CASE xy 01 20 4 xy 01 23 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

15. 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

16. 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

17. What about the Special Case? The only time that the y-intercepts match in perpendicular lines is when they intersect on the y-axis.