Unit 4. Day 3.

Proportional Relationships Unit 4 Proportional Relationships Graphing Equations

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.

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

No steepness No slope

Positive steepness Positive slope

Negative steepness Negative slope

Which bicyclist faces a steeper slope?

Which is steeper?

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

𝑟𝑖𝑠𝑒 Slope: m = 𝑟𝑢𝑛

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

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

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

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

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

Now Y’all Try

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

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

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

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

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

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=4 −5 𝑟𝑖𝑠𝑒 𝑦=4 −5 𝑦=4 −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=4 −5 −3 −3 𝑦= −4 −5 2 2 𝑦=−9 −9 −1 −1

Example J*: 𝑦=−2𝑥+3 𝑟𝑖𝑠𝑒 −4 𝑚= 𝑟𝑢𝑛 2 𝑚=−2 𝑦 𝑥 𝑦=−2 +3 𝑦=−2 +3 𝑦=−2 +3 𝑦=−2 +3 𝑦=−2 +3 𝑦=−2 +3 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

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

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=4 −5 𝑦=4 −5 𝑚=4 𝑦= −5 𝑦= 8 −5 𝑦=−5 −5 𝑦=3 3 𝑦=−17 −17 𝑥 𝑦=4 −5 𝑦= −4 −5 𝑦=−9 −9

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=−2 +3 𝑦=−2 +3 𝑦=−2 +3 𝑦= +3 𝑦= −4 +3 𝑦=3 3 𝑦=−1 −1 𝑚=−2 𝑦=9 9 𝑥

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

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)