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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

3 answers

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.

Find slope
State the meaning of the slope in context

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.