Question

1. the equation $p = 3s$ represents the perimeter $p$ of an equilateral triangle with side length $s$. is there a proportional relationship between the perimeter and the side length of an equilateral triangle? explain.

Explanation:

A proportional relationship is defined by an equation of the form \( y = kx \) where \( k \) is a constant, and the graph passes through the origin. The given equation \( P = 3s \) fits this form with \( k = 3 \), and when \( s = 0 \), \( P = 0 \) (a valid trivial case for side length 0). Thus, perimeter and side length are proportional.

Answer:

Yes, there is a proportional relationship. The equation \( P = 3s \) follows the form \( y = kx \) (proportional relationship) where the constant of proportionality \( k = 3 \), and the relationship passes through the origin.