Practical Applications of Proportional Relationships

This page focuses on applying proportional relationships to real-world scenarios, particularly in the context of speed and distance.

The main example discusses a relationship between distance and time:

y = 45x, where y is distance in miles and x is time in minutes.

Example: To find the speed in miles per minute, we divide 45 by 60 (minutes in an hour), resulting in 0.75 miles per minute.

The page emphasizes that the constant of proportionality (C.O.P.) in this case represents the speed: 0.75 miles per minute.

Highlight: In 1 minute, you will travel 0.75 or 3/4 of a mile.

The page also reinforces the general form of proportional relationships:

Definition: Proportional relationships can be represented by an equation in the form y = kx, where k is the constant of proportionality (C.O.P).

This practical application helps students understand how proportional relationships apply to everyday situations, making it an excellent resource for proportional relationship example problems and proportional relationships explained with examples worksheet exercises.

Representing Proportional Relationships

This page provides a comprehensive overview of how to represent and work with proportional relationships using words, examples, and symbols.

Definition: A linear relationship is proportional when the ratio of y to x is a constant k.

The page presents several examples of proportional relationships in equation form:

1. y = 3x
2. y = kx
3. 9 = 1.28x (where k = 1.28)

Highlight: In a proportional relationship, y = kx, where k ≠ 0 and k is the constant of proportionality (C.O.P.).

A practical example involving yogurt pricing is provided:

Example: If 6 containers of yogurt cost $7.68, we can find the cost per yogurt by dividing: $7.68 ÷ 6 = $1.28 per yogurt. This $1.28 is the constant of proportionality.

The page demonstrates how to use this information to calculate costs for different quantities:

y = 1.28x, so for 10 yogurts: y = 1.28(10) = $12.80

This comprehensive explanation is excellent for understanding proportional relationship characteristics and solving proportional relationship example problems with answers.

Understanding Proportional Relationships

This page introduces the concept of proportional relationships and contrasts them with non-proportional relationships through graphical representations.

A key characteristic of proportional relationships is that their graphs are straight lines passing through the origin (0,0). This visual representation helps students quickly identify whether a relationship is proportional or not.

The page shows two graphs side by side:

1. A proportional relationship graph: A straight line passing through the origin.
2. A non-proportional relationship graph: A line that does not pass through the origin.

Definition: A proportional relationship is a relationship between two quantities where one quantity is always a constant multiple of the other.

Highlight: The graph of a proportional relationship is always a straight line that passes through the origin (0,0).

Example: In the proportional graph shown, as x increases, y increases at a constant rate, forming a straight line through (0,0).

This visual comparison serves as an excellent introduction to proportional relationships explained with examples for 7th grade, helping students grasp the fundamental difference between proportional and non-proportional relationships.