Answer :
To determine the rate of change in the given data, we need to examine the change in the distance (in meters) with respect to the change in time (in minutes).
The table provided is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time in Minutes (x)} & \text{Distance in Meters (y)} \\ \hline 1 & 1,200 \\ \hline 2 & 2,400 \\ \hline 3 & 3,600 \\ \hline 4 & 4,800 \\ \hline \end{array} \][/tex]
Since the data indicates a constant speed, we can pick any two points to calculate the rate of change. We will use the first two points for simplicity.
The formula for the rate of change (which is essentially the slope \( m \)) is given by:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the points \( (1, 1200) \) and \( (2, 2400) \):
[tex]\[ x_1 = 1, \quad y_1 = 1200 \][/tex]
[tex]\[ x_2 = 2, \quad y_2 = 2400 \][/tex]
Plug these values into the formula:
[tex]\[ m = \frac{2400 - 1200}{2 - 1} = \frac{1200}{1} = 1200 \][/tex]
So, the rate of change in the \( y \)-values with respect to the \( x \)-values is:
[tex]\[ 1200 \text{ meters per minute} \][/tex]
Therefore, the correct option is:
[tex]\[ \text{1,200 meters per minute} \][/tex]
The table provided is:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time in Minutes (x)} & \text{Distance in Meters (y)} \\ \hline 1 & 1,200 \\ \hline 2 & 2,400 \\ \hline 3 & 3,600 \\ \hline 4 & 4,800 \\ \hline \end{array} \][/tex]
Since the data indicates a constant speed, we can pick any two points to calculate the rate of change. We will use the first two points for simplicity.
The formula for the rate of change (which is essentially the slope \( m \)) is given by:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the points \( (1, 1200) \) and \( (2, 2400) \):
[tex]\[ x_1 = 1, \quad y_1 = 1200 \][/tex]
[tex]\[ x_2 = 2, \quad y_2 = 2400 \][/tex]
Plug these values into the formula:
[tex]\[ m = \frac{2400 - 1200}{2 - 1} = \frac{1200}{1} = 1200 \][/tex]
So, the rate of change in the \( y \)-values with respect to the \( x \)-values is:
[tex]\[ 1200 \text{ meters per minute} \][/tex]
Therefore, the correct option is:
[tex]\[ \text{1,200 meters per minute} \][/tex]
