Rain fell at a steady rate of 2 inches every 3 hours.

Question

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

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 2

Find slope
State the meaning of the slope in context

Answer 3

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

$$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}$$

where $\mathrm{\Delta }y$ is the change in the y-values (rainfall, in inches) and $\mathrm{\Delta }x$ 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 ($\mathrm{\Delta }y$) and change in x ($\mathrm{\Delta }x$): $$\mathrm{\Delta }y=8-2=6$$ $$\mathrm{\Delta }x=12-3=9$$
3. Calculate the slope ($m$): $$m=\frac{\mathrm{\Delta }y}{\mathrm{\Delta }x}=\frac{6}{9}=\frac{2}{3}$$

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.