Question

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

Explanation:

Step1: Check if the graph passes through the origin

A proportional relationship graph is a straight line that passes through the point \((0,0)\). From the given graph, we can see that the line passes through the origin \((0,0)\), so it satisfies the first condition of a proportional relationship.

Step2: Determine the slope (constant of proportionality)

The formula for the constant of proportionality \(k\) in a proportional relationship \(y = kx\) is \(k=\frac{y}{x}\) (where \(x
eq0\)). Let's pick two points on the line. Let's take a point where \(x = 4\) and find the corresponding \(y\) value. From the graph, when \(x = 4\), \(y = 1\) (assuming the grid has equal units). So \(k=\frac{y}{x}=\frac{1}{4}=0.25\). We can check another point, say \(x = 8\), then \(y = 2\), and \(\frac{y}{x}=\frac{2}{8}=\frac{1}{4}=0.25\). So the constant of proportionality is \(\frac{1}{4}\) (or \(0.25\)).

Answer:

Yes, the graph shows a proportional relationship. The constant of proportionality is \(\frac{1}{4}\) (or \(0.25\)).