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4.3 Proportional Relationships and Graphing

4.3 Proportional Relationships and Graphing. How can you use graphs to represent and analyze proportional relationships?. Graphing Rules. Look at your data Set up your graph Use the ENTIRE graph Plot your points as accurately as possible Label your axis’ Label your graph

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4.3 Proportional Relationships and Graphing

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  1. 4.3 Proportional Relationships and Graphing How can you use graphs to represent and analyze proportional relationships?

  2. Graphing Rules • Look at your data • Set up your graph • Use the ENTIRE graph • Plot your points as accurately as possible • Label your axis’ • Label your graph • Order Pairs (x,y) • Origin (0,0) • Practice Graphing

  3. Explore activity • Complete page 129 Explore Activity with a partner

  4. Identifying Proportional Relationships • Step 1- Create a table • Step 2 – Write the data in the table as ordered pairs (x,y) • Step 3 – Graph the ordered pairs • Plot each point • Draw one line from the origin, connecting points if possible

  5. Example 1 • A house cleaning company charges $45 per hour. Is the relationship a proportional relationship? Explain. • Step 1. Make a table • Step 2. Write the data in the table as ordered pairs (time,cost) • (1,45) (2,90) (3,135) (5,225) (8,360) • Graph the ordered pairs • Step 3 - Look at the graph. Draw the line • The line goes through the origin therefore, it is a proportional relationship. The point (1,45) shows the unit rate is $45 for 1 hour

  6. Your Turn • Page 130 #1

  7. Analyzing Graphs • Proportional relationship is represented with the formula y=kx • In the graph k tells you how steep the graph of the relationship will be. • The larger number k is the steeper your graph will be.

  8. Example 2 • Show graph – The graph shows the relationship between time in minutes and the number of miles Damon runs. Write and equation for this relationship • Step 1 – choose a point on the graph and tell what the point represents • (10,1) (20,2) (30,3) • Step 2- what is the constant of proportionality? • Yes, k= • Step 3 – write an equation in the form of y=kx • y= x

  9. Example 2 reflect • What does the point (0,0) on the graph represent? • The distance (0 miles) that Damon runs in 0 minutes • Suppose you drew a graph representing the relationship y=between time in minutes and the number of miles Esther runs. How would the graph compare to the one for Damon? Explain • Esther’s graph would be steeper; mi/min > mi/min

  10. Your turn • Page 131 #4 a-c

  11. Guided practice • Page 132 # 1-7 • IDK or I don’t know are NOT appropriate answers

  12. Independent Practice • Page 133-134 #1-18

  13. Assessment • 4.3 Assessment • Pg 135 # 1-9 Ready to go on?

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