Question

1. the philadelphia flyers were given two points for each win. is this a proportional relationship?

Explanation:

Step1: Recall proportional relationship definition

A proportional relationship is one where two quantities \( y \) and \( x \) are related by \( y = kx \), where \( k \) is a constant (the constant of proportionality), and when \( x = 0 \), \( y = 0 \) (the graph passes through the origin).

Step2: Define variables for the problem

Let \( x \) be the number of wins, and \( y \) be the total points. The relationship here is \( y = 2x \), since for each win (\( x \)), they get 2 points.

Step3: Check the conditions for proportionality

• The equation is in the form \( y = kx \) with \( k = 2 \) (a constant).
• When \( x = 0 \) (no wins), \( y = 2(0)=0 \) (no points), so the graph passes through the origin.

Answer:

Yes, this is a proportional relationship because the total points \( y \) (dependent variable) and the number of wins \( x \) (independent variable) are related by \( y = 2x \), which fits the form \( y=kx \) (where \( k = 2 \) is a constant) and satisfies \( y = 0 \) when \( x = 0 \).