Ezra observed that the perimeter of a regular pentagon is always 5 times the side length. This means that the relationship between the side length $x$ and the perimeter $y$ can be expressed as:

$y = 5x$

This equation shows a direct proportionality between the side length and the perimeter of the pentagon.

Step 1: Identify two points.

To graph this relationship, we can choose two points that satisfy the equation.

1. When the side length $x = 1$: $y = 5 \times 1 = 5$ So, one point is $(1, 5)$.

2. When the side length $x = 2$: $y = 5 \times 2 = 10$ So, another point is $(2, 10)$.

Step 2: Plot the points and draw the line.

To graph the relationship:

• Plot the point $(1, 5)$ on the graph.
• Plot the point $(2, 10)$ on the graph.
• Draw a straight line through these two points, which extends through the origin $(0, 0)$, since a regular pentagon with a side length of 0 would also have a perimeter of 0.

This line represents the proportional relationship $y = 5x$.

Would you like to see a visual graph of this relationship? I can generate it for you.

Here are 5 related questions:

1. What would be the perimeter if the side length is 3 inches?
2. What is the side length if the perimeter is 25 inches?
3. How does the graph change if the relationship between side length and perimeter changes to $y = 6x$?
4. If Ezra doubles the side length, how does the perimeter change?
5. What is the slope of the line representing this relationship?

Tip: In proportional relationships, the slope of the line is the constant of proportionality, which is the factor by which one quantity scales the other.