1. Slope Between Two Points

2. Table of Contents
8: Warm-Up, Guided Practice
9: How Do I Find the Slope Between Two Points?

3. Warm Up
Write a symbolic representation based on the verbal representation.
1. A cab company chargers a $5 boarding rate in addition to its meter which is $3 for every mile. Write the symbolic representation where C is the total charge and m is the number of miles driven.

4. Learning Intention/Success Criteria
LI: We are learning to find the slope between two points SC: I know how to -graph linear functions represented symbolically as f(x) = mx + b -identify m and b and understand what it means -interpret what m means in context -find m from a table, graph, or ordered pairs -understand how the slope formula relates to numerical and visual representation

5. EQ: How Do I Find the Slope Between Two Points?
5/14/2019

6. Slope
A number used to indicate the steepness of a line and if the line is tilted uphill or downhill
Represented by the letter “m”
m = change in y change in x
Slope Formula
m = y2 – y x2 – x1

7. Example 1: Find the slope between two points:
(3, -4) and (2, 5)
(3, -4) and (2, 5)
(x1, y1)
(x2, y2)
m = y2 – y x2 – x1
m = 5 – – 3
m = – 3
m =
= -9

8. (3, -4) and (2, 5)
Proof
(2, 5)
Rise Run
-9 1 -9 1
(3, -4)

9. Guided Practice 1
Find the slope between the two points: (-4, 2) and (-6, -8)

10. Guided Practice 1 Poll
Find the slope between the two points: (-4, 2) and (-6, -8)
A] 5
B] -5
C] 2
D] 1/5

11. Guided Practice 1 Answer
Find the slope between the two points: (-4, 2) and (-6, -8)
m = y2 – y x2 – x1
m =
m =
m =
= 5

12. Guided Practice 2
Find the slope between the two points: (8, -3) and (0, -1)

13. Guided Practice 2 Poll
Find the slope between the two points: (8, -3) and (0, -1)
A] 1/3
B] -1/4
C] -4
D] -3

14. Guided Practice 2 Answer
Find the slope between the two points: (8, -3) and (0, -1)
m = y2 – y x2 – x1
m =
m =
m =
= -1/4

15. Example 2: Find the slope between two points:
(5, 4) and (5, 1)
(5, 4) and (5, 1)
(x1, y1)
(x2, y2)
m = y2 – y x2 – x1
m =
m =
m = undefined

16. Guided Practice 3
Find the slope between the two points: (-6, 3) and (-7, 3)

17. Guided Practice 3 Poll
Find the slope between the two points: (-6, 3) and (-7, 3)
A] 4/3
B] 3/4
C] undefined
D] zero

18. Guided Practice 3 Answer
Find the slope between the two points: (-6, 3) and (-7, 3)
m = y2 – y x2 – x1
m =
m =
m =
= 0

19. Guided Practice 4
Find the slope between the two points: (-1, -3) and (-1, -5)

20. Guided Practice 4 Poll
Find the slope between the two points: (-1, -3) and (-1, -5)
A] 2/3
B] 1
C] undefined
D] zero

21. Guided Practice 4 Answer
Find the slope between the two points: (-1, -3) and (-1, -5)
m = y2 – y x2 – x1
m =
m =
m =
= undefined

22. Example 3: The table shows the number of miles a plane traveled while in flight. Use the table to find the rate of change.
Time (min)
Distance (mi) 30
290 60
580 90
870
120
1160 x1 y1 x2 y2
m = y2 – y x2 – x1
m =
m =
m = 9.66

23. What does the slope mean in context?
y x
Miles flown Minutes flying
Miles flown Minutes flying
The plane flies 9.66 miles every minute.

24. Guided Practice 5
The table below shows the number of small packs of fruit snacks, F(b), per box, b. Find the slope of the line and explain what it means in context.
Boxes (b) 3 5 7 9
Packs, F(b) 24 40 56 72

25. Guided Practice 5 Poll
Find the slope of the table
A] -8
B] -1/8
C] 8
D] 1/8

26. Guided Practice 5 Answers
Find the slope of the table x2 x1
Boxes (b) 3 5 7 9
Packs, F(b) 24 40 56 72
m = y2 – y x2 – x1 y2 y1
m = 8
m =
m =
There are 8 packs per box