https://file.aiquickdraw.com/mathbot/file/172610340721850a5ndxb.jpg

Let's break down the problem from the image and work through it.

### Given Data:
The table shows the number of boxes and corresponding number of bandages:

| # of Boxes | 2  | 3  | 5  | 7  |
|------------|----|----|----|----|
| # of Bandages | 24 | 36 | 60 | 84 |

### 1. **Rate of Change:**
The rate of change is calculated as the difference in the number of bandages divided by the difference in the number of boxes.

Using the two points (2, 24) and (3, 36):
\[
\text{Rate of change} = \frac{36 - 24}{3 - 2} = \frac{12}{1} = 12
\]

Thus, the rate of change is **12** bandages per box.

### 2. **Equation:**
Since the relationship between boxes and bandages is linear (as evident from the constant rate of change), the equation follows the form:
\[
y = mx + b
\]
where:
- \( m \) is the rate of change (12).
- \( b \) is the y-intercept (value of y when x = 0).

Using one of the given points, say (2, 24):
\[
24 = 12(2) + b \implies 24 = 24 + b \implies b = 0
\]

Thus, the equation is:
\[
y = 12x
\]
where \( y \) is the number of bandages and \( x \) is the number of boxes.

### 3. **Plotting the Graph:**
- The points from the table (2, 24), (3, 36), (5, 60), and (7, 84) should be plotted on the graph, where the x-axis represents the number of boxes and the y-axis represents the number of bandages.

The graph should show a straight line passing through these points, with a slope of 12.

Would you like further details on how to draw the graph, or do you need help with anything else?

### 5 Related Questions:
1. How can you determine if the relationship between two variables is linear from a table of values?
2. What does the slope of the line represent in the context of this problem?
3. If there were 10 boxes, how many bandages would there be according to the equation?
4. How would the graph change if the rate of change were different?
5. What would the y-intercept represent if it were not zero?

### Tip:
When determining the rate of change from a table, always ensure that you pick points with consistent intervals to verify the relationship is linear.

Use the information in the table to complete the graph and answer the questions. The table shows the number of boxes and corresponding number of bandages: | # of Boxes | 2  | 3  | 5  | 7  | | # of Bandages | 24 | 36 | 60 | 84 |

Learn how to calculate the rate of change and form the linear equation from a table of values showing the number of boxes and bandages. The rate of change is 12 bandages per box, and the equation is y = 12x. Suitable for students in Grades 6-8.

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