1. Warm Up Identify which lines are parallel.
y = 6; y = 6x + 5; y = 6x – 7; y = -8
Identify which lines are perpendicular
y = 3x – 4; y = x + 2; y = -1; x = 3

2. Objectives Identify and graph parallel and perpendicular lines.
Write equations to describe lines parallel or perpendicular to a given line.

3. Vocabulary
parallel lines
perpendicular lines

4. Directions:
Write an equation in slope-intercept form for the line that is parallel to the given line and that passes through the given point.

5. Example 1
y = 3x + 8; (4, 10)
Step 1 Find the slope of the line.
y = 3x + 8
The slope is 3.
The parallel line also has a slope of 3.
Step 2 Write the equation in point-slope form.
y – y1 = m(x – x1)
Use the point-slope form.
Substitute 3 for m, 4 for x1, and 10 for y1.
y – 10 = 3(x – 4)

6. Example 1 Continued
Step 3 Write the equation in slope-intercept form.
y – 10 = 3(x – 4)
y – 10 = 3x – 12)
Distribute 3 on the right side.
y = 3x – 2
Add 10 to both sides.

7. Example 2
y = x – 6; (5, 7)
Step 1 Find the slope of the line.
The slope is .
y = x –6
The parallel line also has a slope of .
Step 2 Write the equation in point-slope form.
y – y1 = m(x – x1)
Use the point-slope form.

8. Example 2 Continued
Step 3 Write the equation in slope-intercept form.
Distribute on the right side.
Add 7 to both sides.

9. Directions:
Write an equation in slope-intercept form for the line that is perpendicular to the given line and that passes through the given point.

10. Example 3
y = 2x – 5; (2, –1).
Step 1 Find the slope of the line.
y = 2x – 5
The slope is 2.
The perpendicular line has a slope of because
Step 2 Write the equation in point-slope form.
y – y1 = m(x – x1)
Use the point-slope form.
Substitute for m, –1 for y1, and 2 for x1.

11. Example 3 Continued
Step 3 Write the equation in slope-intercept form.
Distribute on the right side.
Subtract 1 from both sides.

12. Example 4
y = 5x; (–5, 3)
Step 1 Find the slope of the line.
y = 5x
The slope is 5.
The perpendicular line has a slope of because .
Step 2 Write the equation in point-slope form.
y – y1 = m(x – x1)
Use the point-slope form.

13. Example 4 Continued
Step 3 Write in slope-intercept form.
Distribute on the right side.
Add 3 to both sides.

14. Lesson Summary
Write an equation is slope-intercept form for the line described.
1. contains the point (8, –12) and is parallel to
2. contains the point (4, –3) and is perpendicular to y = 4x + 5