https://file.aiquickdraw.com/mathbot/file/1726031404766zegska6z.jpg

Let's go over the questions one by one from the image:

### Question 5: Create a Graph and Draw a Curve
You need to create a graph of the data points in the table and then draw a curve that connects the points. The graph provided in the image has a coordinate plane with "Design Number" on the x-axis and "Number of Tiles" on the y-axis. To complete this, plot the points from your table (which isn't shown but seems to be related to the designs and tiles), then connect them smoothly.

### Question 6: Make Sense of the Points
The question asks if all the points on the curve make sense in terms of the problem. The answer depends on whether the number of tiles behaves consistently with the pattern of design growth. Think about whether it's possible for the design numbers and tile counts to behave linearly or exponentially, and if any data points seem unrealistic for the problem context (e.g., negative values, sudden jumps, etc.).

### Question 7: Identify the Pattern
You are asked to describe the pattern as linear, exponential, quadratic, or none. Based on the graph in the image (though it's incomplete), you should check how the "Number of Tiles" changes with the "Design Number." If it's a constant rate of change, it's linear. If the change is proportional to the current value, it's exponential. If the rate of change increases consistently (second degree), it's quadratic.

### Question 8: Hyatt Home Improvement Tile Design
The empty sign is **10 feet tall and 12 feet wide**, so the total area is:
\[
\text{Area} = 10 \times 12 = 120 \text{ square feet}.
\]
Since each tile measures **1 foot by 1 foot**, the number of tiles that fit the sign is **120 tiles**. Thus, the largest design that can fit on the sign requires **120 tiles**.

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Do you need details or explanations on any part of this? Here are 5 related questions:

1. How would you determine if a graph shows a linear, quadratic, or exponential relationship?
2. How do you check if all points on a curve make sense in the context of a problem?
3. What are the steps to plot points and create a smooth curve in a graph?
4. What are the key differences between linear and quadratic growth patterns?
5. How do you calculate the area when working with real-world objects like signs or tiles?

**Tip:** When identifying patterns in data, always look at the differences between consecutive values.

5. Create a graph of the data points in your table on the coordinate plane. Draw a curve to connect the points.
6. Do all of the points on the curve make sense in terms of the problem situation? Explain your reasoning.
7. Describe the pattern as linear, exponential, quadratic, or none of these. Explain your reasoning.
8. The owner of Hyatt Home Improvement wants to put one of their designs on an empty rectangular sign in front of their headquarters. The empty sign is 10 feet tall and 12 feet wide. When he uses square tiles measuring 1 foot by 1 foot, what is the number of the largest design that fits on the sign? How many tiles does that design require?

Explore graphing and data analysis by plotting design numbers and tile counts, identifying patterns like linear, quadratic, or exponential. Additionally, calculate the area of a rectangular sign using square tiles. This exercise involves graph interpretation and real-world area calculation, suitable for Grades 6-8.

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