1. 3.3 Slopes of Lines

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

3. What is Slope?
The slope (m) of a line is the number of units the line rises or falls for each unit of horizontal change from left to right.
In other words, slope is the ratio of vertical rise or fall to its horizontal run.
m =
rise
run

4. The Slope Formula y2 - y1 m = x2 - x1
In algebra, we also learned a formula for slope called the slope formula.
y2 - y1
m =
x2 - x1
Remember to keep your subtraction of the coordinates in the proper order.
CORRECT
y2 - y1
Subtraction order is the same
x2 - x1
INCORRECT
y2 - y1
Subtraction order is different
x1 - x2

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

6. Example 1b: Find the slope of the line. Use the slope formula.
Let be and be
Answer: undefined

7. Example 1c:
Find the slope of the line.
Answer:

8. Example 1d:
Find the slope of the line.
Answer: 0

9. Slopes of ║ and  Lines
Finally, recall from algebra that lines which are║ or  have mathematical relationships.
║ lines have the same slope. i.e. If line l has a slope of ¾ and line m is ║to line l then it also has a slope of ¾.
 lines have opposite reciprocal slopes.
i.e. If line a has a slope of 2 and line b is  to line a then it has a slope of – ½.

10. Slope Postulates
Postulate 3.2 Two non-vertical lines have the same slope if they are ║.
Postulate 3.3 Two non-vertical lines are  if the product of their slopes is -1.

11. Example 3a:
Determine whether and are parallel, perpendicular, or neither.

12. Example 3a:
The slopes are not the same, The product of the slopes is
are neither parallel nor perpendicular.
Answer:

13. Example 3b:
Determine whether and are parallel, perpendicular, or neither.
Answer: The slopes are the same, so
are | | .

14. Your Turn: a. b.
Determine whether and are parallel, perpendicular, or neither.
Answer: perpendicular
Answer: neither

15. Example 4:
Graph the line that contains Q(5, 1) and is parallel to with M(–2, 4) and N(2, 1).
Slope formula
Substitution
Simplify.

16. Example 4: The slopes of two parallel lines are the same.
The slope of the line parallel to
Answer:
Graph the line.
Start at (5, 1). Move up 3 units and then move left 4 units.
Label the point R.

17. Your Turn:
Graph the line that contains R(2, –1) and is parallel to with O(1, 6) and P(–3, 1).
Answer:

18. Assignment
Pg #16-32 (evens)