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Linear Relationships, SM-Bank 039 MC

Pepper uses matchsticks to make a pattern of shapes, as shown in the table below.
 

 
The equation used to show the relationship between  \(T\)  and  \(N\)  is

  1. \(T = N + 1\)
  2. \(T = 6N\)
  3. \(T = 6N+2\)
  4. \(T = 6N-4\)
Show Answers Only

\(D\)

Show Worked Solution

\(T\ \text{increases by 6 each shape.}\)

\(\text{Consider}\ T = 6N – 4:\)

\(\text{When}\ \ N = 1,\ T = 6\times 1 − 4 = 2\)

\(\text{When}\ \ N = 2, \ T = 6\times − 4 = 8\)

\(\text{When}\ \ N = 3,\ T = 6\times − 4 = 14\)

\(\therefore T = 6N − 4\ \text{is correct}\)

\(\Rightarrow D\)