Question

d. write an equation to represent the proportional relationship between the school’s cost of a uniform and the amount a student must pay for a lost uniform. use u to represent the uniform cost and s to represent the amount a student must pay for a lost uniform. what is the constant of proportionality?

Explanation:

Step1: Define Proportional Relationship

In a proportional relationship, the equation is of the form \( s = k \cdot u \), where \( k \) is the constant of proportionality. Here, \( s \) is the student's payment amount and \( u \) is the uniform's cost. Since the student pays the full cost of the lost uniform (proportional, same as school's cost), the constant \( k = 1 \).

Step2: Formulate the Equation

Using the proportional relationship formula \( y = kx \) (here \( s = k u \)), with \( k = 1 \), the equation is \( s = u \). The constant of proportionality \( k \) is 1 because the student's payment equals the uniform's cost (direct proportion with ratio 1:1).

Answer:

The equation is \( s = u \), and the constant of proportionality is \( 1 \).