Question

this table shows the number of tiles used to create a pattern.

\

$$\begin{tabular}{|c|c|} \\hline \\text{position number} & \\text{number of tiles} \\\\ \\hline 1 & 8 \\\\ \\hline 2 & 11 \\\\ \\hline 3 & 14 \\\\ \\hline 4 & 17 \\\\ \\hline 5 & 20 \\\\ \\hline \\end{tabular}$$

barney claims that this data represents a linear relation. is he correct?

( ) yes
( ) no

Explanation:

Analyze the given data table

We examine the relationship between the position number \(x\) and the number of tiles \(y\).
The values from the table are:

• For \(x = 1\), \(y = 8\)
• For \(x = 2\), \(y = 11\)
• For \(x = 3\), \(y = 14\)
• For \(x = 4\), \(y = 17\)
• For \(x = 5\), \(y = 20\)

Calculate the first differences

To determine if the relation is linear, we calculate the differences between consecutive \(y\)-values.

• \(11 - 8 = 3\)
• \(14 - 11 = 3\)
• \(17 - 14 = 3\)
• \(20 - 17 = 3\)

Determine if the relation is linear

Since the first differences are constant, the rate of change is constant.
This confirms that the relation is linear.
Therefore, Barney's claim is correct.

Answer:

• yes (Correct answer)
• no