1. Unit 4. Day 3.

2. Proportional Relationships
Unit 4
Proportional Relationships
Graphing
Equations

3. Please get out paper for today’s lesson
Name
Date
Period
Topic: Introduction to Slope
Understand the connections between proportional relationships, lines, and linear equations.

4. Today’s Lesson
1) Introduce Slope
2) Practice finding slope
3) Graph and find slope

5. No steepness
No slope

6. Positive steepness
Positive slope

7. Negative steepness
Negative slope

8. Which bicyclist faces a steeper slope?

9. Which is steeper?

10. Which bicyclist faces a steeper slope?
1 3
5 15 7 21
6 15
2 5 8 20

11. 𝑟𝑖𝑠𝑒
Slope:
m =
𝑟𝑢𝑛

13. Today’s Lesson
1) Introduce Slope
2) Practice finding slope
3) Graph and find slope

14. 𝑦
Example A*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒
2 3 6
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 9 𝑥

15. 𝑦
Example B*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 6
3 1
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 2 𝑥

16. 𝑦
Example C*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒
− 3 5 −6
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 10 𝑥

17. 𝑦
Example D*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 −4
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 1
𝑚=−4 𝑥

18. Now Y’all
Try

19. 𝑦
Example E*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 9
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 6
𝑚= 3 2 𝑥

20. 𝑦
Example F*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 1
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 1
𝑚=1 𝑥

21. 𝑦
Example G*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 −5
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 4
𝑚=− 5 4 𝑥

22. 𝑦
Example H*:
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 −4
𝑟𝑖𝑠𝑒 𝑚=
𝑟𝑢𝑛 2
𝑚=− 2 1 𝑥

24. Today’s Lesson
1) Introduce Slope
2) Practice finding slope
3) Graph and find slope

25. Example I*: 𝑦=4𝑥−5 8 𝑟𝑖𝑠𝑒 𝑚= 𝑟𝑢𝑛 2 𝑚=4 𝑦 𝑥 𝑦=4 −5 𝑦=4 −5 𝑦=4 −5 𝑦= −5
𝑦= −5
𝑟𝑖𝑠𝑒
𝑦= −5
𝑦= −5 𝑚=
𝑟𝑢𝑛 2 𝑦= −5 𝑦=
−12 −5 𝑦= 8 −5
𝑦=−5 −5
𝑦=3 3
𝑦=−17
𝑚=4
−17 𝑥 𝑥 𝑦
𝑦= −5 −3 −3 𝑦= −4 −5 2 2
𝑦=−9 −9 −1 −1

26. Example J*: 𝑦=−2𝑥+3 𝑟𝑖𝑠𝑒 −4 𝑚= 𝑟𝑢𝑛 2 𝑚=−2 𝑦 𝑥 𝑦=−2 +3 𝑦=−2 +3 𝑦=−2 +3
𝑦=−
𝑦=−
𝑦=− 𝑚=
𝑟𝑢𝑛 2 𝑦= +3 𝑦= +6 +3 𝑦= −4 +3
𝑦=3 3
𝑦=−1 −1
𝑚=−2
𝑦=9 9 𝑥 𝑥 𝑦 −3 −3 2 2

27. Example K* 2𝑦 2𝑦−3𝑥=10 2𝑦−3𝑥=10 = 10 +3𝑥 +3𝑥 +3𝑥 𝑟𝑖𝑠𝑒 3 𝑦 𝑚= + 𝑟𝑢𝑛 2 =𝑦=
+3𝑥
+3𝑥
+3𝑥
𝑟𝑖𝑠𝑒 3 𝑦= −3 +5 𝑦 𝑚= +
𝑟𝑢𝑛 2 = 2
𝑦=2 2 2
𝑚= 3 2 𝑦=
3 2 𝑥
+ 5 𝑦= +5 𝑥
𝑦=5 5 𝑥 𝑦 𝑦= −2 −2 𝑦= 3 +5
𝑦= 3 2 𝑥+5 2 2
𝑦=8 8

28. Example I*: 𝑦=4𝑥−5 𝑚=4 𝑦=4 −5 𝑦=4 −5 𝑦= −5 𝑦= 8 −5 𝑦=−5 −5 𝑦=3 3 𝑦=−17
𝑦= −5
𝑦= −5
𝑚=4 𝑦= −5 𝑦= 8 −5
𝑦=−5 −5
𝑦=3 3
𝑦=−17
−17 𝑥
𝑦= −5 𝑦= −4 −5
𝑦=−9 −9

29. Example J*: 𝑦=−2𝑥+3 𝑚=−2 𝑦=−2 +3 𝑦=−2 +3 𝑦=−2 +3 𝑦= +3 𝑦= −4 +3 𝑦=3 3
𝑦=−
𝑦=−
𝑦=− 𝑦= +3 𝑦= −4 +3
𝑦=3 3
𝑦=−1 −1
𝑚=−2
𝑦=9 9 𝑥

30. Example K* 2𝑦 2𝑦−3𝑥=10 2𝑦−3𝑥=10 = 10 +3𝑥 +3𝑥 +3𝑥 𝑦 + = 2 2 𝑚= 3 2𝑦=
+3𝑥
+3𝑥
+3𝑥 𝑦= −3 +5 𝑦 + = 2
𝑦=2 2 2
𝑚= 3 2 𝑦=
3 2 𝑥
+ 5 𝑦= +5 𝑥
𝑦=5 5 𝑦= 𝑦= 3 +5
𝑦= 3 2 𝑥+5
𝑦=8 8

31. Assumption of the Virgin (1514)
Today’s Assignment:
Graph & find slope
𝑦=2𝑥−4
𝑦=3𝑥−4
2𝑦+6𝑥=8
6𝑥−3𝑦=15
Assumption of the Virgin (1514)