### Student Page 2.9.4 Analyzing More Tile Patterns

Study the visual patterns in Figure 2.9.4.1. Assume each pattern continues infinitely and grows predictably. Determine the following for each pattern:

#### 1.

How is the pattern growing? Use colors or numbers to show how tiles are added to the pattern from one step to the next. Show how the pattern builds from one step to the next.

#### 2.

Draw Step 5. Draw Step 0.

#### 3.

For each step, determine the number of tiles needed.

#### 4.

Determine if the pattern is proportional linear, linear, or other. Explain your decision.

#### 5.

For each linear and proportional linear pattern,

##### (a)

Find an equation that gives the number of tiles in a step based on its step number.

##### (b)

Determine what part of the pattern relates to the slope. Explain your choice.

##### (c)

Determine what part of the pattern relates to the y-intercept. Explain your choice.