Question

1. does the graph show a proportional relationship? if so, find the constant of proportionality.

Explanation:

Step1: Check proportional relationship

A proportional relationship graph is a straight line passing through the origin \((0,0)\). The given graph is a straight line and passes through the origin, so it shows a proportional relationship.

Step2: Find constant of proportionality

The constant of proportionality \(k\) for a proportional relationship \(y = kx\) is calculated as \(k=\frac{y}{x}\). Let's take a point on the line, for example, when \(x = 2\), \(y = 2\) (assuming grid units, we can also take other points like \(x = 1,y = 1\) or \(x=- 2,y = - 2\)). Then \(k=\frac{y}{x}=\frac{2}{2} = 1\) (or using \(x = 1,y = 1\), \(k=\frac{1}{1}=1\)).

Answer:

Yes, the graph shows a proportional relationship. The constant of proportionality is \(1\).