1. Splash Screen

2. Five-Minute Check (over Lesson 3–2) CCSS Then/Now New Vocabulary
Key Concept: Slope of a Line
Example 1: Find the Slope of a Line
Concept Summary: Classifying Slopes
Example 2: Real-World Example: Use Slope as Rate of Change
Postulates: Parallel and Perpendicular Lines
Example 3: Determine Line Relationships
Example 4: Use Slope to Graph a Line
Lesson Menu

3. Mathematical Practices 4 Model with mathematics.
Content Standards
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Mathematical Practices
4 Model with mathematics.
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
CCSS

4. Use slope to identify parallel and perpendicular lines.
You used the properties of parallel lines to determine congruent angles.
Find slopes of lines.
Use slope to identify parallel and perpendicular lines.
Then/Now

5. slope
rate of change
Vocabulary

6. Concept

7. Concept

8. A. Find the slope of the line.
Find the Slope of a Line
A. Find the slope of the line.
Substitute (–3, 7) for (x1, y1) and (–1, –1) for (x2, y2).
Slope formula
Substitution
Simplify.
Answer: –4
Example 1

9. B. Find the slope of the line.
Find the Slope of a Line
B. Find the slope of the line.
Substitute (0, 4) for (x1, y1) and (0, –3) for (x2, y2).
Slope formula
Substitution
Simplify.
Answer: The slope is undefined.
Example 1

10. C. Find the slope of the line.
Find the Slope of a Line
C. Find the slope of the line.
Substitute (–2, –5) for (x1, y1) and (6, 2) for (x2, y2).
Slope formula
Substitution
Simplify.
Answer:
Example 1

11. D. Find the slope of the line.
Find the Slope of a Line
D. Find the slope of the line.
Substitute (–2, –1) for (x1, y1) and (6, –1) for (x2, y2).
Slope formula
Substitution
Simplify.
Answer: 0
Example 1

12. A. Find the slope of the line.B. C. D.
Example 1a

13. B. Find the slope of the line.
A. 0
B. undefined
C. 7 D.
Example 1b

14. C. Find the slope of the line.A. B.
C. –2
D. 2
Example 1c

15. D. Find the slope of the line.
A. 0
B. undefined
C. 3 D.
Example 1d

16. Concept

17. Step 1 Find the slopes of and .
Determine Line Relationships
Determine whether and are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer.
Step 1 Find the slopes of and
Example 3

18. Step 2 Determine the relationship, if any, between the lines.
Determine Line Relationships
Step 2 Determine the relationship, if any, between the lines.
The slopes are not the same, so and are not parallel. The product of the slopes is So, and are not
perpendicular.
Example 3

19. Answer: The lines are neither parallel nor perpendicular.
Determine Line Relationships
Answer: The lines are neither parallel nor perpendicular.
Check When graphed, you can see that the lines are not parallel and do not intersect in right angles.
Example 3

20. Determine whether AB and CD are parallel, perpendicular, or neither for A(–2, –1), B(4, 5), C(6, 1), and D(9, –2)
A. parallel
B. perpendicular
C. neither
Example 3

21. Use Slope to Graph a Line
Graph the line that contains Q(5, 1) and is parallel to MN with M(–2, 4) and N(2, 1).
First, find the slope of
Slope formula
Substitution
Simplify.
Example 4

22. The slopes of two parallel lines are the same.
Use Slope to Graph a Line
The slopes of two parallel lines are the same.
The slope of the line parallel to through Q(5, 1) is
Answer:
Graph the line.
Start at (5, 1). Move up 3 units and then move left 4 units.
Label the point R.
Draw
Example 4

23. Graph the line that contains R(2, –1) and is parallel to OP with O(1, 6) and P(–3, 1).
A. B.
C. D. none of these
Example 4

24. End of the Lesson