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Proportional Webs

Proportional Webs

Author: Rebecca Newburn
Description:

Many relationships are proportional. Learn how to identify them.

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Tutorial

Questions to think about:

  • What is a proportional relationship?
  • How can I tell if the relationship is proportional?

Proportional Relationships

A proportional relationship is when the growth pattern is multiplied by a scale factor.

Situation
We'll be exploring how a relationship can be expressed in a situation. For example, Malia buys bird 1 lb. of bird seed for $3. If she buys 2 lbs., she would spend $6. Since she is charged the same amount per pound, and there is no initial fee, this is a proportional relationship.

Table
Malia's Birdseed

Lbs 1 2 3 4
Cost ($) 3 6 9 12

You can write each point as a fraction in simplest terms and if they are all equal, then it's a proportion. Ex. 1 third equals 2 over 6 equals 3 over 9 equals 4 over 12 because they all simplify to 1 third.

Graph
You can tell if a graph is proportional because it is 1) linear (a line) and 2) goes through the origin (0, 0).

Equation
The relationship between the quantities can be written in the form of y = kx. k is the constant of proportionality. The constant of proportionality is the same as the scale factor.


Proportional or Not Proportional?

For equations, the equation is in the form of y = kx. k is the constant of proportionality. The instructor mentioned that if it is a one-step equation it's proportional. NOTE: y = x + k, which is a one-step equation, is NOT proportional. Only one step equations in the form y = kx are proportional.

Source: Danielle Kunetz

Source: Ms. Newburn