To determine the rate of change (or speed) given a table showing distance traveled over time, you first need to identify the change in distance (Δy) and the change in time (Δx). The rate of change is given by the formula:
\[ \text{Rate of change} = \frac{\Delta y}{\Delta x} \]
Where:
- \(\Delta y\) is the change in distance (meters)
- \(\Delta x\) is the change in time (minutes)
Without the specific values from the table, let's assume you have sample data points. For example, suppose that at time \( t_1 \) (in minutes), the distance is \( d_1 \) (in meters), and at time \( t_2 \) (in minutes), the distance is \( d_2 \) (in meters).
The rate of change (or speed) can be calculated as follows:
1. Find the difference in distances:
\[ \Delta y = d_2 - d_1 \]
2. Find the difference in times:
\[ \Delta x = t_2 - t_1 \]
3. Compute the rate of change:
\[ \text{Rate of change} = \frac{\Delta y}{\Delta x} \]
Given your options:
- minutes per meter
- minutes per meter
- 900 meters per minute
- 1,200 meters per minute
These options suggest speed in meters per minute, not minutes per meter. This implies we are looking for a positive rate compared to elapsed time.
Let's verify with an example.
Suppose the distance traveled in 5 minutes is 6,000 meters, and the travel at the start is 0 meters. The table might give points (0 minutes, 0 meters) and (5 minutes, 6,000 meters).
\[ \Delta y = 6,000 \text{ meters} - 0 \text{ meters} = 6,000 \text{ meters} \]
\[ \Delta x = 5 \text{ minutes} - 0 \text{ minutes} = 5 \text{ minutes} \]
\[ \text{Rate of change} = \frac{6,000 \text{ meters}}{5 \text{ minutes}} = 1,200 \text{ meters per minute} \]
Hence, according to the options given, the rate of change in the y-values with respect to the x-values is:
\[ 1,200 \text{ meters per minute} \]
The table shows the distance traveled over time while traveling at a constant speed.
What is the rate of change in the y-values with respect to the x-values?
minutes per meter
minutes per meter
900 meters per minute
1,200 meters per minute
1 answer