1. Lesson 3-3
Slopes of Lines

2. Standardized Test Practice:
Transparency 3-3
5-Minute Check on Lesson 3-2
In the figure, m4 = 146. Find the measure of the following angles. 2 7
10
4. 11
5. Find m11 + m6
In the figure to the right what is the measure of ABC?
146
34
146
34
180
Standardized Test Practice: A A
77 B
84 C
89 D
91

3. Objectives Find slopes of lines
Use slopes to identify parallel and perpendicular lines

4. Vocabulary
Slope – symbol m; the vertical rise divided by the horizontal run (or m = y/x) A horizontal line has a slope of zero (no change in y; y = 0) A vertical line has an undefined slope (no change in x; x = 0)
Rate of change – describes how a quantity changes over time

5. Postulates
3.2 – Two non-vertical lines have the same slope if, and only if, they are parallel.
3.3 – Two non-vertical lines are perpendicular if, and only if, the product of their slopes is -1.

6. Review of Slopes
Slope, m, is a rate of change (∆y / ∆x) between two points (x1, y1) and (x2, y2) y x
y2 – y ∆y
m = =
x2 – x ∆x
Two lines are parallel (never intersect), if they have the same slope (myellow = 1)
Two lines are perpendicular (forms a right angle), if their slopes multiply together to get -1 (mpink = -1)

7. Find the slope of the line.
From (–3, 7) to (–1, –1), go down 8 units and right 2 units.
Answer: – 4

8. Find the slope of the line.
Use the slope formula.
Let be and be
Answer: undefined

9. Find the slope of the line.
Answer:

10. Find the slope of the line.
Answer: 0

11. a. Find the slope of the line.
Answer:

12. b. Find the slope of the line.
Answer: 0

13. c. Find the slope of the line.
Answer: 2

14. d. Find the slope of the line.
Answer: undefined

15. RECREATION For one manufacturer of camping equipment, between 1990 and 2000, annual sales increased by $7.4 million per year. In 2000, the total sales were $85.9 million. If sales increase at the same rate, what will be the total sales in 2010?
Slope formula

16. Simplify.
Multiply each side by 10.
Add 85.9 to each side.
The coordinates of the point representing the sales for 2010 are (2010, 159.9).
Answer: The total sales in 2010 will be about $159.9 million.

17. Determine whether and are parallel, perpendicular, or neither.
The slopes are not the same, The product of the slopes is
are neither parallel nor perpendicular.
Answer:

18. Determine whether and are parallel, perpendicular, or neither.
Answer: The slopes are the same, so are parallel.

19. a. b.
Determine whether and are parallel, perpendicular, or neither.
Answer: perpendicular
Answer: neither

20. Summary & Homework Summary:
The slope of the line is the ratio of its vertical rise to its horizontal run
Parallel lines have the same slope
Perpendicular lines have slopes whose product is -1 (also known as negative inverses)
Homework: pg : 15, 16, 19, 20, 25, 27, 29, 30