1. Homework: Maintenance Sheet 15 via study island due Friday

3. Constant of Proportionality
I can interpret a unit rate (using words and mathematically).
I can analyze proportional relationships and use them to solve real world problems.
Unit Rate
Constant of Proportionality

4. Number of items purchased (x)
Example 1: A school dance committee purchases identical party favors for a school dance. Five students bought different numbers of favors at different times. Each paid the same price per favor. Information on the purchases is shown in the table below.
Identify and interpret the constant of proportionality ( 𝒚 𝒙 ) based on situation.
Number of items purchased (x) 10 20 12 16 8
Total Cost in $ (y) 5 6 4
I can interpret a unit rate (using words and mathematically).
I can analyze proportional relationships and use them to solve real world problems.

5. You can represent proportional relationships in several ways:
I can interpret a unit rate (using words and mathematically). I can analyze proportional relationships and use them to solve real world problems.
In a proportional relationship, two quantities vary directly with each other. y = kx and k = 𝑦 𝑥
You can represent proportional relationships in several ways:
An equation in the form y = kx, where k is the constant of proportionality or unit rate.
A graph of a straight line that passes through the origin
A set or table of ordered pairs that show equivalent ratios
A verbal description that describes a directly proportional relationship between two quantities

6. Distance Driven (in miles)
I can interpret a unit rate (using words and mathematically). I can analyze proportional relationships and use them to solve real world problems.
Example 2: A car technician took a car on four test drives. For each drive, the technician recorded the miles driven and the amount of gas used.
Does the data in the table represent a proportional relationship?
Gallons of gas used
Distance Driven (in miles) 4
100 2 50 1 25
0.5 12

7. Representing Proportional Relationships
Write and simplify each data pair from the table
Are the ratios the same?
Does the data in the table represent a proportional relationship?

8. Example 3: Do the points on the graph represent a proportional relationship? Explain how you know.

9. Representing Proportional Relationships
Find the values of the ratio 𝑦 𝑥 .

10. What does the x-axis or horizontal axis represent?
Example 4: The graph below shows the resting heart rate of the number of heartbeats per second.
What does the x-axis or horizontal axis represent?
What does the y-axis or vertical axis represent?
What is the number of beats per second (unit rate).
Write an equation to represent the relationship.
I can interpret a unit rate (using words and mathematically).
I can analyze proportional relationships and use them to solve real world problems.