Final answer:
To analyze proportional relationships based on ordered pairs, find the constant of proportionality by dividing y by x, identify the independent variable that affects the dependent variable, calculate the dependent variable by multiplying the independent variable with the constant of proportionality, and graph the relationship resulting in a straight line through the origin if it's directly proportional.
Step-by-step explanation:
When analyzing ordered pairs that represent a proportional relationship, it's essential to identify several components:
A. Constant of Proportionality
The constant of proportionality (k) is found when two variables are directly proportional (y = kx). To determine k, divide the y-value by the x-value for any given pair (assuming x is not zero).
B. Independent Variable
The independent variable is the variable that you change to see how it affects the other variable. It's typically represented on the x-axis of a graph.
C. Dependent Variable
The dependent variable changes in response to the independent variable, and it's typically illustrated on the y-axis. In a direct relationship, this variable is calculated by multiplying the independent variable by the constant of proportionality.
D. Graphing the Relationship
To graph a proportional relationship, plot the ordered pairs on a coordinate plane, and if the relationship is direct, you should see a straight line passing through the origin (0,0).