Math Problem Statement

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.

Solution

The problem in the image discusses a proportional relationship between the side length xx of a regular pentagon and its perimeter yy. Specifically, Ezra finds that the perimeter is always 5 times the side length. This gives the equation:

y=5xy = 5x

Here, xx represents the side length in inches, and yy represents the perimeter in inches. To graph this proportional relationship, you will need two points where y=5xy = 5x. Let's choose two points:

  1. When x=0x = 0, y=5(0)=0y = 5(0) = 0, so the point is (0,0)(0, 0).
  2. When x=2x = 2, y=5(2)=10y = 5(2) = 10, so the point is (2,10)(2, 10).

Now, you can draw a straight line passing through these two points (0,0)(0, 0) and (2,10)(2, 10) to represent the relationship y=5xy = 5x.

Do you want further explanation or more details about graphing or proportional relationships?

Here are five related questions to consider:

  1. What would the perimeter be for a pentagon with a side length of 4 inches?
  2. How does the graph of this relationship compare to the graph of y=2xy = 2x?
  3. If the side length is doubled, how does that affect the perimeter?
  4. What other polygons have a perimeter that is proportional to their side length?
  5. How would the graph change if the pentagon had a different ratio between the perimeter and side length?

Tip: In proportional relationships like this, the graph is always a straight line that passes through the origin.

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Math Problem Analysis

Mathematical Concepts

Proportional Relationships
Graphing Linear Equations

Formulas

y = 5x

Theorems

Proportionality Theorem

Suitable Grade Level

Grade 6-8