In this section we will compare the graphs of proportional and non-proportional relationships.

Look at the data tables from the example in the first section of the lesson.

Company A

Number of Songs	Cost to Download
5	$4.95
10	$9.90
15	$14.85
20	$19.80
25	$24.75
30	$29.70
35	$34.65
40	$39.60
45	$44.55
50	$49.50

Company B

Number of Songs	Cost to Download
5	$22.45
10	$24.90
15	$27.35
20	$29.80
25	$32.25
30	$34.70
35	$37.15
40	$39.60
45	$42.05
50	$44.50

Let’s explore what the graphs of proportional and non-proportional relationships look like. Use this link to complete the activity.

Instructions

Enter the data from the first two columns of the company A data table in the window below the graph.
To enter the data, you can highlight all the numbers in both columns and then copy and paste the data into the window, or you can enter each data pair separately with a comma between the numbers.
Click the ‘update plot’ button at the bottom of the applet.
Check the ‘display line of best fit’ box on the right side of the applet.

Where does the line of best fit cross the y-axis?
Interactive popup. Assistance may be required. Check Your Answer It crosses at the origin (0,0)

Click the reset button
Repeat the steps for the data in the first two columns of the company B data table

Where does the line of best fit cross the y-axis?
Interactive popup. Assistance may be required. Check Your Answer It crosses at (0,20)

Click the reset button.
Repeat the steps with the data from the second proportional example from section 1:

weeds	pay
10	$0.25
20	$0.50
30	$0.75
40	$1.00
50	$1.25
60	$1.50
70	$1.75
80	$2.00

Where does the line of best fit cross the y-axis?
Interactive popup. Assistance may be required. Check Your Answer It crosses at the origin (0,0)

What does the answer to the previous question tell you about the graphs of proportional relationships?
Interactive popup. Assistance may be required. Check Your Answer Graphs of proportional relationships will pass through the origin.

Click the reset button
Use the applet to determine which of the following data tables showing the price list for mulch from two landscaping companies represents a proportional relationship.

Landscape Central

Cubic Yards of Mulch	Price
1	$35.50
2	$71.00
3	$106.50
4	$142.00
5	$177.50

Mulch-R-Us

Cubic Yards of Mulch	Price
1	$35.00
2	$65.00
3	$95.00
4	$125.00
5	$155.00

Which company uses a proportional relationship in their price list?
Interactive popup. Assistance may be required. Check Your Answer Landscape Central

How did you know?
Interactive popup. Assistance may be required. Check Your Answer The graph for Landscape Central passes through (0, 0).
The graph for Mulch-R-Us crosses the y-axis at (0, 5).