1. POD Do the following numbers represent a proportional relationship?
cost 8 16 22 30
# of pizzas 1 2 3 4

2. POD
Day 2
Which of the following graphs represents a proportional relationship? Explain. a. b.

3. 1-5 Graph Proportional Relationships
The coordinate plane is a type of grid that is formed when two number lines intersect at their zero points.
The number lines separate the coordinate plane into four regions called quadrants.

4. An ordered pair is a pair of numbers, such as (1,2), used to locate or graph points on the coordinate plane.
The x-coordinate corresponds to a number on the x-axis
(1,2)
The y-coordinate corresponds to a number on the y-axis
y-axis
origin
x-axis

5. Another way to determine whether two quantities are proportional is to graph the quantities on the coordinate plane. If the graph of the two quantities is a straight line through the origin, then the two quantities are proportional.

6. Example 1:
The slowest mammal on Earth is the tree sloth. It moves at a speed of 6 feet per minute. Determine whether the number of feet the sloth moves is proportional to the number of minutes it moves by graphing on the coordinate plane
Time (min) 1 2 3 4
Distance (ft) 6 12 18 24
The line passes through the point of origin and is a straight line. So the number of feet traveled is proportional to the number of minutes.

7. Example 2:
James earns $5 an hour babysitting. Determine whether the amount of money James earns babysitting is proportional to the number of hours he babysits by graphing on the coordinate plane.
Time (min) 1 2 3 4
Amount ($) 5 10 15 20
The graph is a straight line through the origin, therefore the amount of money is proportional to the number of hours.

8. Example 3:
The cost of renting video games from Games Inc. is shown in the table. Determine whether the cost is proportional to the number of games rented by graphing on the coordinate plane.
Number of games
cost 1 3 2 5 7 4 9
The line does not pass through the origin. So, the cost of video games is not proportional to the number of games rented.

9. Example 4:
Cole went to the store to buy transformer toys. The prices for the toys are listed in the chart below. Use the coordinate plane to determine if the cost of the toys is proportional to the number of toys.
Number of Transformers
cost 1
$4.50 2
$9.00 3
$12.50 4
$14.00
These values do not represent a proportional relationship.

10. Example 5:
Graham was training for a marathon and set up a training schedule. Use the coordinate plane to determine if the number of miles he ran is proportional to the amount of time he ran?
Miles
Time (hr) 8 1 14 2 20 3 24 4
These values do not represent a proportional relationship.

11. Example 6:
Grace works as a waitress and gets paid in tips. Use the coordinate plane to determine if the amount of money she earns is proportional to the number of hours worked.
Time (hrs) 1 2 3 4 5
Amount ($) 15 30 45 60 75
These values represent a proportional relationship.