Question

the graphs show some properties of regular polygons. when compared with the independent variable, how many of the graphs represent a linear relationship? # of diagonals from 1 vertex y number of sides x 0 1 3 2

Explanation:

Step1: Recall linear - relationship criteria

A linear relationship has a constant rate of change and its graph is a straight - line.

Step2: Analyze the given graph

The points on the graph are \((3,0)\), \((4,1)\), \((5,2)\), \((6,3)\). The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For \((3,0)\) and \((4,1)\), \(m=\frac{1 - 0}{4 - 3}=1\). For \((4,1)\) and \((5,2)\), \(m=\frac{2 - 1}{5 - 4}=1\). For \((5,2)\) and \((6,3)\), \(m=\frac{3 - 2}{6 - 5}=1\). The rate of change is constant and if we were to connect the points, we would get a straight - line.

Answer:

1