https://file.aiquickdraw.com/mathbot/file/1727280958433d3g1jqlv.jpg

Let's analyze the image you provided step by step:

### Table and Graph Information:
The table shows the **height (ft)** of an elevator at different **time intervals (s)**. The graph plots this data.

#### Table:
- At \( t = 0 \, \text{seconds} \), height = 0 ft
- At \( t = 1 \, \text{second} \), height = 20 ft
- At \( t = 2 \, \text{seconds} \), height = 40 ft
- At \( t = 3 \, \text{seconds} \), height = 60 ft
- At \( t = 4 \, \text{seconds} \), height = 80 ft

#### Graph:
- The **x-axis** represents **time in seconds (s)**.
- The **y-axis** represents **height in feet (ft)**.
- The points plotted correspond to the values in the table, forming a straight line indicating uniform movement of the elevator.

### Filling in the Multiple-Choice Options:
1. **The x-axis represents the**: 
   - **time in seconds** (as noted by "Time (s)" on the table and x-axis label).

2. **The y-axis represents the**:
   - **height of the elevator in feet** (as indicated by the "Height (ft)" label).

3. **The x-axis has a scale of 1 mark =**:
   - From the graph, 1 mark on the x-axis corresponds to **1 second**.

4. **The y-axis has a scale of 1 mark =**:
   - On the y-axis, 1 mark represents **10 feet** (since the points increment by 20 ft, and there are 2 marks between each increment).

5. **The origin (0, 0) represents a height of**:
   - At \( t = 0 \, \text{seconds} \), the height is **0 feet**, as seen in the table and graph.

Would you like further details or explanations on this? Here are some related questions that might help expand on the concept:

### 5 Related Questions:
1. What is the rate of change of the elevator’s height over time?
2. How would the graph look if the elevator started at a height of 20 ft instead of 0 ft?
3. What is the equation of the line that represents the height of the elevator over time?
4. How would the graph change if the elevator moved faster, increasing its height by 40 ft every second?
5. What would happen to the graph if the elevator descended at the same rate?

### Tip:
To determine the slope of the line in a time vs. height graph, divide the change in height by the change in time!

Analyze the graph showing the height of an elevator over time and answer the following: What does the x-axis represent? What does the y-axis represent? What is the scale on both axes? What does the origin represent?

This problem explains how to read and analyze a linear graph showing the height of an elevator as it rises over time. Learn key concepts like the slope of the line, scale of axes, and how to interpret the origin. Suitable for middle school students, Grades 6-8.

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