Question

2aps-8
reasoning the equation below describes a proportional relationship between x and y. what is the constant of proportionality? use pencil and paper. explain why your answer is called the \constant of proportionality.\
y = 7.19x
the constant of proportionality is \boxed{}.

Explanation:

Step1: Recall the formula for proportional relationships

A proportional relationship between two variables \( x \) and \( y \) is represented by the equation \( y = kx \), where \( k \) is the constant of proportionality. This constant \( k \) is the ratio of \( y \) to \( x \) (\( k=\frac{y}{x} \)) and remains constant for all corresponding values of \( x \) and \( y \) in the relationship.

Step2: Identify the constant of proportionality from the given equation

The given equation is \( y = 7.19x \). Comparing this with the general form of a proportional relationship \( y = kx \), we can see that the value of \( k \) (the constant of proportionality) is \( 7.19 \). This is because in the equation \( y = 7.19x \), the coefficient of \( x \) is \( 7.19 \), which corresponds to \( k \) in the general form. So, this coefficient is the constant ratio between \( y \) and \( x \), meaning that for any value of \( x \), \( y \) will be \( 7.19 \) times that \( x \), and this ratio stays the same (constant) for all pairs of \( x \) and \( y \) that satisfy the equation.

Answer:

\( 7.19 \)