# Proportional and Non-proportional Relationships

The focus of this lesson is comparing and contrasting proportional and non-proportional relationships. You may recall that in proportional relationships, the variables in the problem are related by a constant factor or ration.

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? How did you know? # Review and Practice—Which One is Proportional? Now try the following example problems. The prices for sliced ham from the deli section of four different grocery stores are listed below. Compare the price lists, and determine which grocery store is using a proportional relationship to price their sliced ham. Store A  Pounds Price 0.5$3.50 1 $6.50 1.5$9.50 2 $12.50 Store B  Pounds Price 0.5$2.75 1 $5.00 1.5$7.50 2 $10.00 Store C  Pounds Price 0.5$3.25 1 $6.50 1.5$9.75 2 $13.00 Store D  Pounds Price 0.5$3.00 1 $6.00 1.5$9.00 2 \$11.00

Copy the following tables into your notes, and fill in the missing information for each store.

Store A

 Pounds Price price/ pound 0.5 1 1.5 2

Store B

 Pounds Price price/ pound 0.5 1 1.5 2

Store C

 Pounds Price price/ pound 0.5 1 1.5 2

Store D

 Pounds Price price/ pound 0.5 1 1.5 2

1. Is this the store that uses a proportional relationship to determine the price of sliced ham?

2. How do you know?

1. Is this the store that uses a proportional relationship to determine the price of sliced ham?

2. How do you know?

1. Is this the store that uses a proportional relationship to determine the price of sliced ham?

2. How do you know?

1. Is this the store that uses a proportional relationship to determine the price of sliced ham?

2. How do you know?

Four students measured the height of plants they were growing in their science class. They measured the height of the plants each week for four weeks.  Their results are shown in the data table below:

 Name Height of the plant (centimeters) Week 1 Week 2 Week 3 Week 4 Mario 2.0 5.0 8.0 10.0 Suzie 1.0 1.5 2.5 4.0 Frank 2.5 5.0 7.5 10.0 Shantel 1.5 3.5 5.5 7.5

1. Which student had a plant that showed growth proportional to the number of weeks?

2. How did you know?