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4-37.

Examine the $x→y$ table below.

Figure
Number

Number of
Tiles

$0$

$5$

$1$

$9$

$2$

$13$

$3$

$17$

1. Invent a tile pattern that fits this data.

Possible Patterns

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure $0$

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure $1$

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure $2$

 tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$ tile $\space$

Figure $3$

2. How is the pattern growing?  Show where the pattern of growth appears in the $x→y$ table and the tile pattern.

 FigureNumber Number ofTiles $0$ $5$ $\color{orange}{\Big)} \color{blue}{+4}\\$ From 5 tiles to 9 tiles is plus 4$\color{orange}{\Big)} \color{blue}{+4}\\$ From 9 tiles to 13 tiles is plus 4$\color{orange}{\Big)} \color{blue}{+4}\\$ From 13 tiles to 17 tiles is plus 4. $1$ $9$ $2$ $13$ $3$ $17$

3. Write a rule for this pattern.

Write an equation in $y=mx+b$ form.

Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: 4-37 HW eTool