1. Evaluating a graph of a proportional relationship Friday, September 12

2. Learning Target I will be able to: explain the unit rate (constant of proportionality) on graphs and equations; identify unit rates on a proportional graph and explain points such as (0,0) and (1,r); and represent the proportional relationship as an equation in the form y=kx.

3. Evaluating the graph What is the title on the graph? An amount of money paid to someone for selling something. What is a commission? Typical jobs where commissions are earned: Sales jobs—who can give an example? Real Estate – earn commissions on the sale of a home Professional sports agents: http://www.forbes.com/sites/jasonbelzer/2013/07/31/the-worlds-most- powerful-sports-agents/ http://www.forbes.com/sites/jasonbelzer/2013/07/31/the-worlds-most- powerful-sports-agents/

4. Evaluating the graph What is represented on the x-axis on this graph? What does the point (80,6) on the graph mean? What is represented on the y- axis on this graph? The coordinate pair on the graph are represented as (x,y) In this case what is x? What does the 80 mean? What is the y value that is given on this graph? What does the 6 mean? The 80 represents the amount of the purchase. The 6 represents the commission earned on $80 of purchases. If purchases were $160, how much would the commission be? If purchases were $40, how much would commission be?

5. Characteristics of a proportional graph Proportional graphs have straight lines These graphs must go through the origin (0,0). The point on the graph where x = 1 indicates the unit rate (1,r)

6. Finding the unit rate The point on the graph where x = 1 indicates the unit rate (1,r) What is the unit rate: It is the value of y when x=1.

7. Can you write the equation for this graph?

8. Identifying characteristics of a proportional graph What does the point (0,0) mean on this graph? What does the point (1,r) represent on the graph? Is the point (1,r) the same as (1,x)? (0,0) It means that when you first start (zero time) the sloth has not gone any distance. (1,r) = (1,6) r = unit rate or 6 feet/minute Yes they are the same value, but in proportional graphs, r means that it is the unit rate.

9. Can you write the equation for this graph?

10. Identifying characteristics of a proportional graph What does the point (0,0) mean on this graph? What is represented on the x-axis? What is represented on the y-axis? It means that for zero dollars you would get 0 pounds US Dollars British pounds Exchange rate US dollars to British pounds What does this point represent? It means that for $3 you could exchange it for 2 British pounds.

11. Identifying characteristics of a proportional graph How can we find the unit rate (1,r) on this graph? We could start with the rate of 2/3 and change it to a unit rate. Exchange rate US dollars to British pounds

12. Can you write the equation for this graph?

13. Identifying characteristics of a proportional graph What does the point (0,0) mean on this graph? What is represented on the x-axis? What is represented on the y-axis? It means that for zero web visits you would have 0 downloads. Number of web visits. Number of downloads. Exchange rate US dollars to British pounds What does this point represent? It means that for 24 web visits you would have 8 downloads

14. Identifying characteristics of a proportional graph How can we find the unit rate (1,r) on this graph? We could start with the rate of 4/12 and change it to a unit rate.

15. Can you write the equation for this graph?

16. Rate your learning I will be able to: explain the unit rate (constant of proportionality) on graphs and equations; identify unit rates on a proportional graph and explain points such as (0,0) and (1,r); and represent the proportional relationship as an equation in the form y=kx.