Recall that a proportional relationship can be represented in a table, in an equation, verbally, or graphically. A constant of proportionality is the constant value of the ratio between two proportional quantities.
In this lesson, we will compare two different proportional relationships represented by graphs, equations, and tables in order to determine which has a greater rate of change.
In order to compare proportional relationships represented in different ways, we start by identifying the unit rate (or slope) from the graphs, tables, or equation.
Given an equation of proportional relationship:
Which describes a greater unit rate of change of y with respect to x?
Relationship A:
y=5x
Relationship B:
x | 0 | 1 | 2 | 3 |
---|---|---|---|---|
y | 0 | 4.5 | 9 | 13.5 |
Which describes a greater unit rate of change of y with respect to x?
Relationship A:
Relationship B:
x | 2 | 4 | 6 | 8 |
---|---|---|---|---|
y | 12 | 24 | 36 | 48 |
When comparing proportional relationships, we need to compare the unit rate of change represented by the slope of the line. Equations written in the form y=mx are handy because they are the easiest form to identify the slope of the line from.
If we don't have the equation of the line we can use the following to find the slope from the coordinates of two identified points: