4.3 Proportional Relationships and Graphing

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Presentation transcript:

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 Order Pairs (x,y) Origin (0,0) Practice Graphing

Explore activity Complete page 129 Explore Activity with a partner

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

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 $45 for 1 hour Time (hr) 1 2 3 5 8 Cost ($) 45 90 135 225 360

Your Turn Page 130 #1

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.

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= 𝑦 𝑥 Step 3 – write an equation in the form of y=kx y= 1 10 x

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= 1 8 𝑥 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; 1 8 mi/min > 1 10 mi/min

Your turn Page 131 #4 a-c

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

Independent Practice Page 133-134 #1-18

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