Chapter 4.2, Problem 2P

For each diagram, find the relationship between the number of shapes and the perimeter of the figure they form. Represent this relationship using a table, words, an equation, and a graph.

To determine

To Fill: The table for perimeter for squares n.

Answer to Problem 2P

  

Explanation of Solution

Given information: 1 square has 4 units as perimeter, 2 squares has 6 units and 3 squares has 8 units and so on.

Calculation:

If we see the difference of y values they are increasing by 2 while x values are increasing by 1.

So, we can fill the next three boxes by increasing 2 from it’s previous value.

  

Now, let’s find the number of squares which has 22 as it’s perimeter.

Let’s continue the rule

Number of squares	Perimeter
7	16
8	18
9	20
10	22

  

Now, let’s find the rule.

Take two points on the table and find the rule

(1,4) (3,8)

Slope $m=\frac{8-4}{3-1}=\frac{4}{2}=2$

Plug in this value into $y=mx+b$

It gives $y=2x+b$

Using (1,4)

  $\begin{array}{l}4=2(1)+b\\ 4=2+b\end{array}$

Subtract both sides 2

  $b=2$

The rule is $y=2x+2$

Here, we need to use variable ‘ n’ for ‘ x’.

So, the rule is $2n+2$ .