Ezra is finding the perimeter of different-sized regular pentagons. He finds the perimeter is always 5 times longer than the side length.

There is a proportional relationship between the side length of the regular pentagon in 

inches,
 
x

,

 and the perimeter of the regular pentagon in 

inches,
 
y

.

Graph this relationship. Select two points to draw a line.

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.

Explore the proportional relationship between the side length and perimeter of regular pentagons. Learn how to graph this relationship with step-by-step examples and understand its implications in geometry. Suitable for Grades 6-8 students.

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