Proportional and Non-proportional Relationships 3-6 Notes for Algebra 1 Proportional and Non-proportional Relationships

Proportional Relationships If its equation is of the form 𝑦=𝑘𝑥 and 𝑘≠0. The graph will pass through 0, 0 .

Example 1 pg. 198 Proportional Relationships ENERGY The table shows the number of miles driven for each hour of driving. 1.) Graph the data. What can you deduce from the pattern about the relationship between the number of hours of driving h and the number of miles driven m. 2.) Write an equation to describe this relationship. 3.) Use this equation to predict the number of miles driven in 8 hours. Hours 1 2 3 4 Miles 50 100 150 200

Example 1 pg. 198 Proportional Relationships ENERGY The table shows the number of miles driven for each hour of driving. 1.) Graph the data. What can you deduce from the pattern about the relationship between the number of hours of driving h and the number of miles driven m. There is a linear relationship between the hours of driving and miles driven. Hours 1 2 3 4 Miles 50 100 150 200 250 200 150 100 50 1 2 3 4 5

Example 1 pg. 198 Proportional Relationships ENERGY The table shows the number of miles driven for each hour of driving. 2.) Write an equation to describe this relationship. 𝑚=50ℎ 3.) Use this equation to predict the number of miles driven in 8 hours. 400 miles Hours 1 2 3 4 Miles 50 100 150 200

Non-Proportional Relationships A linear function that does not pass through 0, 0

Example 2 pg. 199 Non-Proportional Relationships Write an equation in function notation for the graph. 16 14 12 10 8 6 4 2 1 3 5

Example 2 pg. 199 Non-Proportional Relationships Write an equation in function notation for the graph. 𝑓 𝑥 =3𝑥−2 16 14 12 10 8 6 4 2 1 3 5

3-6 pg. 200 5-13o, 21-33