Short Answer 
To determine if a relationship between two variables is proportional, check if equations can be expressed as one variable being a constant multiplied by another. After identifying potential proportional relationships, verify them by calculating whether the output maintains a consistent ratio for various inputs. Understanding that proportionality means constant ratios is essential for analyzing these relationships correctly.
Identify Proportional Relationships
To find whether a relationship between two variables is proportional, you need to analyze their equations. Proportional relationships can typically be expressed in the form of equations where one variable can be expressed as a constant multiplied by another variable. The following tables represent such relationships:
- Table 1: y = 3.5x
- Table 2: y = 1/3 x
- Table 3: y = 5x
Verify with Calculations
Once you identify potential proportional relationships, it’s essential to verify them through calculations. You can check the relationship by plugging in values for x and seeing if the output for y maintains the ratio. Here’s how to check each table:
- For Table 1, with x = 2, y = 3.5(2) = 7
- For Table 2, with x = 3, y = 1/3(3) = 1
- For Table 3, with x = 3, y = 5(3) = 15
Understand the Concept of Proportionality
Understanding the concept of proportion is crucial in recognizing these relationships. Proportionality means that two ratios or fractions are equal; thus the variables in a proportional relationship have constant ratios. When analyzing these relationships, confirm that all ratios between corresponding values are equivalent, ensuring that the nature of proportionality holds true throughout your calculations.