1. 5.6 Parallel and Perpendicular Lines
Section 5.6

2. Rules and Properties Parallel Lines
5.6 Parallel and Perpendicular Lines
Rules and Properties
Parallel Lines
If two different lines have the same slope, the lines are parallel.
Just remember,
Parallel lines have the same slope!

3. Rules and Properties Perpendicular Lines
5.6 Parallel and Perpendicular Lines
Rules and Properties
Perpendicular Lines
If the slopes of two lines are m and , the
lines are perpendicular. m 1 –
Perpendicular lines, have opposite reciprocal slopes

4. 5.6 Parallel and Perpendicular Lines
Key Skills
Write an equation in slope-intercept form for the line that contains the point (0, 9) and is parallel to the line x – 5y = 4. 1 5 4
y = x –
slope-intercept form
x – 5y = 4 1 5
m = 1 5
y = x + 9
b = 9

5. 5.6 Parallel and Perpendicular Lines
Key Skills
Write an equation in slope-intercept form for the line that contains the point (0, 5) and is parallel to the line 2x + 3y = 7.
2x + 3y = 7
slope-intercept form 2 3 –
m =
b = 5

6. 5.6 Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that contains the point (4, -1) and is parallel to the line y = 2x + 1, using the point-slope form.
y – (-1) = 2(x – 4)
y = 2x + 1
y + 1 = 2x – 8
m = 2
y – y1 = m(x – x1)
y = 2x – 9

7. 5.6 Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that contains the point (2, -1) and is parallel to the line y = 2x + 2, using the point-slope form.
y – (-1) = 2(x – 2)
y = 2x + 2
y + 1 = 2x – 4
m = 2
y – y1 = m(x – x1)
y = 2x – 5

8. 5.6 Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that contains the point (3, 3) and is parallel to the line y = x – 1, using the point-slope form.
2 3
2 3
2 3
y – 3 = (x – 3)
y = x – 1
2 3
2 3
y – 3 = x – 2
m =
2 3
y – y1 = m(x – x1)
y = x + 1

9. 5.6 Parallel and Perpendicular Lines
Key Skills
Write an equation in slope-intercept form for the line that contains the point (0, 9) and is perpendicular to the line x – 5y = 4. 1 5 4
y = x –
x – 5y = 4
slope-intercept form
opposite reciprocal
of : –5 1 5
m = –5
y = –5x + 9
b = 9

10. 5.6 Parallel and Perpendicular Lines
Key Skills
Write an equation in slope-intercept form for the line that contains the point (0, 5) and is perpendicular to the line y = –8x + 4.
m =
y = –8x + 4
y = x + 5
b = 5
Opposite reciprocal
of -8 is

11. 5.6 Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that contains the point (-3, 1) and is perpendicular to the line y = –3x + 7.
y – y1 = m(x – x1)
y = –3x + 7
y – 1 = (x – (-3))
Opposite reciprocal
of -3 is
y – 1 = x + 1
m =
y = x + 2

12. 5.6 Parallel and Perpendicular Lines
Write an equation in slope-intercept form for the line that contains the point (-2, 7) and is perpendicular to the line 2x – 5y = 3.
2x – 5y = 3
y – y1 = m(x – x1)
– 5y = –2x + 3
y – 7 = – (x – (-2))
– –5
y – 7 = – (x + 2)
y = x –
y – 7 = – x – 5
m =
m = –
y = – x + 2

13. Section 5.6: page 261 – 262 # 18 – 39 (every 3rd), 40 – 55, 58 – 61
Assignment
Section 5.6:
page 261 – 262
# 18 – 39 (every 3rd),
40 – 55, 58 – 61