Question

Rain fell at a steady rate of 2 inches every 3 hours.
Complete the table to describe the relationship.


Time(h)
3




12
Rainfall (in.)


4
6



Graph the data in the table on the coordinate plane grid. Draw the line

Answer 1

Find slope
State the meaning of the slope in context

Answer 2

To complete the table and describe the relationship between time (in hours) and rainfall (in inches), we can use the following relationship:

- The rate of rainfall is 2 inches every 3 hours.

From this rate, we can determine the rainfall corresponding to different times.

**Calculating Rainfall:**

1. **For 3 hours:**
\[
\text{Rainfall} = 2 \, \text{inches}
\]

2. **For 4 hours:**
\[
\text{Rainfall} = \left( \frac{2\, \text{inches}}{3\, \text{hours}} \right) \times 4\, \text{hours} = \frac{8}{3} \approx 2.67 \, \text{inches}
\]

3. **For 6 hours:**
\[
\text{Rainfall} = \left( \frac{2\, \text{inches}}{3\, \text{hours}} \right) \times 6\, \text{hours} = 4 \, \text{inches}
\]

4. **For 12 hours:**
\[
\text{Rainfall} = \left( \frac{2\, \text{inches}}{3\, \text{hours}} \right) \times 12\, \text{hours} = 8 \, \text{inches}
\]

**Completed Table:**

| Time (h) | Rainfall (in.) |
|----------|-----------------|
| 3 | 2 |
| 4 | 2.67 |
| 6 | 4 |
| 12 | 8 |

### Graphing the Data:

To graph the data, plot the points corresponding to the table:

- (3, 2)
- (4, 2.67)
- (6, 4)
- (12, 8)

### Drawing the Line:

Once you've plotted the points on the graph, you can draw a line connecting these points, indicating the steady increase in rainfall over the time interval.

### Note:

If you're doing this in a classroom setting or using software, simply draw axes where the x-axis represents time in hours and the y-axis represents rainfall in inches. Plot the points accordingly and then connect them with a straight line to represent this linear relationship.

Answer 3

To find the slope of a linear relationship, we can use the formula for slope \( m \):

\[
m = \frac{\Delta y}{\Delta x}
\]

where \(\Delta y\) is the change in the y-values (rainfall, in inches) and \(\Delta x\) is the change in the x-values (time, in hours).

From the data we have:

- When \( x = 3\, \text{hours} \), \( y = 2\, \text{inches} \)
- When \( x = 12\, \text{hours} \), \( y = 8\, \text{inches} \)

We can calculate the slope using these two points:

1. **Choose two points:** (3, 2) and (12, 8)
2. **Calculate change in y (\(\Delta y\)) and change in x (\(\Delta x\)):**
\[
\Delta y = 8 - 2 = 6
\]
\[
\Delta x = 12 - 3 = 9
\]
3. **Calculate the slope (\( m \)):**
\[
m = \frac{\Delta y}{\Delta x} = \frac{6}{9} = \frac{2}{3}
\]

### Meaning of the Slope in Context

The slope of \( \frac{2}{3} \) indicates that for every 3 hours that pass, the rainfall increases by 2 inches.

In practical terms, this means that the rain is falling at a steady rate of **2 inches every 3 hours**, which translates to a rate of about **0.67 inches per hour**. This provides a clear understanding of how quickly the rainfall accumulates over time based on the established rate.