1. Lesson 3-3 Menu In the figure, m 4 = 146. 1.Find m 2. 2.Find m 7. 3.Find m 10. 4.Find m 11. 5.Find m 11 + m 6. 6.In the figure, what is the measure of ABC?

2. Lesson 3-3 Ideas/Vocabulary Find slopes of lines. slope Use slope to identify parallel and perpendicular lines. rate of change

3. Lesson 3-3 Key Concept 1

4. Lesson 3-3 Example 1 A. Find the slope of the line. Find the Slope of a Line From (–3, 7) to (–1, –1), go down 8 units and right 2 units. Answer:

5. Lesson 3-3 Example 1 B. Find the slope of the line. Find the Slope of a Line Use the slope formula. Let (0, 4) be (x 1, y 1 ) and (0, –3) be (x 2, y 2 ). which is undefined. Answer:undefined

6. Lesson 3-3 Example 1 C. Find the slope of the line. Find the Slope of a Line Answer:

7. Lesson 3-3 Example 1 D. Find the slope of the line. Find the Slope of a Line Answer:0

8. Lesson 3-3 CYP 1a A. A B. B C. C D. D A. Find the slope of the line.

9. Lesson 3-3 CYP 1b A. A B. B C. C D. D B. Find the slope of the line. 0 undefined 7

10. Lesson 3-3 CYP 1c A. A B. B C. C D. D C. Find the slope of the line. –2 2

11. Lesson 3-3 CYP 1d A. A B. B C. C D. D D. Find the slope of the line. 0 undefined 3

12. Lesson 3-3 Example 2 RECREATION For one manufacturer of camping equipment, between 1995 and 2005 annual sales increased by $7.4 million per year. In 2005, the total sales were $85.9 million. If sales increase at the same rate, what will be the total sales in 2015? Let (x 1, y 1 ) = (2005, 85.9) and m = 7.4. m = 7.4, y 1 = 85.9, x 1 = 2005, and x 2 = 2015 Use Rate of Change to Solve a Problem Slope formula

13. Lesson 3-3 Example 2 Answer: The total sales in 2015 will be about $159.9 million. Use Rate of Change to Solve a Problem Add 85.9 to each side. Simplify. Multiply each side by 10. The coordinates of the point representing the sales for 2015 are (2015, 159.9).

14. Lesson 3-3 Postulates 1

15. Lesson 3-3 Example 3 Determine Line Relationships Find the slopes of and. A. Determine whether and are parallel, perpendicular, or neither. F(1, –3), G(–2, –1), H(5, 0), J(6, 3)

16. Lesson 3-3 Example 3 Determine Line Relationships Answer:The slopes are not the same, so and are not parallel. The product of the slopes is So, and are neither parallel nor perpendicular.

17. Lesson 3-3 Example 3 Determine Line Relationships B. Determine whether and are parallel, perpendicular, or neither. F(4, 2), G(6, –3), H(–1, 5), J(–3, 10) Answer: The slopes are the same, so and are parallel.

18. Lesson 3-3 CYP 3a A. Determine whether and are parallel, perpendicular, or neither. A(–2, –1), B(4, 5), C(6, 1), D(9, –2) A. A B. B C. C parallel perpendicular neither

19. Lesson 3-3 CYP 3b B. Determine whether and are parallel, perpendicular, or neither. A(7, –3), B(1, –2), C(4, 0), D(–3, 1) A. A B. B C. C parallel perpendicular neither

20. Lesson 3-3 Example 4 Use Slope to Graph a Line First find the slope of. Graph the line that contains Q(5, 1) and is parallel to with M(–2, 4) and N(2, 1). Slope formula Substitution Simplify.

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

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