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. because they all simplify to
.
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.
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