Overview
This lesson explains how to find the constant of proportionality using tables and simple formulas, and how to write equations for proportional relationships.
Understanding the Constant of Proportionality
- The constant of proportionality is the ratio between two proportional quantities.
- It is usually represented by ( k ) in the equation ( y = kx ).
- The formula for ( k ) is ( k = \frac{y}{x} ).
- ( y ) is the value from the y-column, and ( x ) is the value from the x-column.
Example Problems
- To find ( k ), divide a y-value by its corresponding x-value.
- Example 1: if ( y = 8 ) and ( x = 1 ), then ( k = \frac{8}{1} = 8 ).
- Example 2: ( y = 16 ) and ( x = 2 ), so ( k = \frac{16}{2} = 8 ).
- In a proportional table, ( k ) remains the same for all rows.
- After finding ( k ), substitute it into ( y = kx ) to write the equation (e.g., ( y = 8x )).
Practice Problem from Worksheet
- Given ( y = 12 ), ( x = 2 ): ( k = \frac{12}{2} = 6 ).
- Substitute ( k ) into the equation: ( y = 6x ).
- This equation models the relationship shown in the table.
Key Terms & Definitions
- Constant of Proportionality — The ratio ( k ) that relates proportional y and x values; calculated as ( k = \frac{y}{x} ).
- Proportional Relationship — A relationship where one quantity is a constant multiple of another, expressed as ( y = kx ).
Action Items / Next Steps
- Complete practice problems on the constant of proportionality worksheet.
- Review the definition and formula for the constant of proportionality.