7.8 Parallel and Perpendicular LinesStandard 8.0: Understand the concepts of parallel and perpendicular lines and how their slopes are related.

Vocabulary

Parallel Lines – Lines that never cross and never intersect.

Perpendicular Lines – Lines that, when they cross each other, form right angles.

Steps for determining if graphs are parallel or perpendicular

1. Put both equations into slope-intercept form.

2. Find the slope and y-intercept of each equation.

3. Analyze the slope and y-interceptParallel – Slope is the same; y-intercept differentPerpendicular – Slope is a negative reciprocal

Finding Opposite ReciprocalsFinding Opposite Reciprocals

a)a) -3-3b)b) 1/31/3c)c) -2/5-2/5d)d) 66e)e) -3/2-3/2f)f) -1/6-1/6g)g) 88h)h) 3/83/8i)i) 7/37/3

a)a) 1/31/3b)b) -3-3c)c) 5/25/2d)d) -1/6-1/6e)e) 2/32/3f)f) 66g)g) -1/8-1/8h)h) -8/3-8/3i)i) -3/7-3/7

#1 Determine whether the graphs of the equations are parallel lines

yx 43 83 xy

43 xy 83 xy

3m 4b 3m 8b

different? intercepts-y theand same theslopes theAre

#2 Determine whether the graphs of the equations are parallel lines

xy 24 463 yx

yx 42 436 xy

2m 4b2

1m

3

2b

Neither

42 xy6

4

6

3

6

6

xy

3

2

2

1 xy

#3 Determine whether the graphs of the equations are perpendicular lines

352 yx 625 yx

325 xy 652 xy

5

2m

5

3b 2

5m 3b

5

3

5

2

5

5

xy

2

6

2

5

2

2

xy

32

5 xy

5

3

5

2 xy

#4 Determine whether the graphs of the equations are perpendicular lines

54 xy 2312 xy

2312 xy

4

1m

4

5b 4

1m

6

1b

4

5

4

1

4

4xy

12

2

12

3

12

12xy

6

1

4

1 xy4

5

4

1 xy

#5 Write an equation for the line containing the given point and perpendicular to the given line.

3m

b 22

b 63

12

b 4

43

1 xy

43 xy

3

1mbmxy

);2,6(