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

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= 𝑦 𝑥
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= 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; 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 #1-18

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