Answer :
To determine the practical meaning of the slope in this situation, let us analyze the given data for the plane's descent:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time, } x \text{ (min.)} & \text{Altitude, } y \text{ (km)} \\ \hline 0 & 12 \\ \hline 2 & 10 \\ \hline 4 & 8 \\ \hline 6 & 6 \\ \hline 8 & 4 \\ \hline 10 & 2 \\ \hline \end{array} \][/tex]
Step-by-step solution to find the slope:
1. Identify two points on the graph: Let's use the first two points [tex]\((0, 12)\)[/tex] and [tex]\((2, 10)\)[/tex].
2. Calculate the slope [tex]\( m \)[/tex] using the formula for the slope of a line through two points:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1) = (0, 12)\)[/tex] and [tex]\((x_2, y_2) = (2, 10)\)[/tex].
3. Plug in the values:
[tex]\[ m = \frac{10 - 12}{2 - 0} = \frac{-2}{2} = -1 \][/tex]
4. Interpret the slope:
- The slope [tex]\( m = -1 \)[/tex] means the altitude decreases by 1 kilometer for every 1 minute that passes. In other words, the plane descends.
Thus, the practical meaning of the slope is:
[tex]\[ \text{a. For every minute that passes the airplane descends 1 kilometer.} \][/tex]
Therefore, the correct answer is:
a. For every minute that passes the airplane descends 1 kilometer.
[tex]\[ \begin{array}{|c|c|} \hline \text{Time, } x \text{ (min.)} & \text{Altitude, } y \text{ (km)} \\ \hline 0 & 12 \\ \hline 2 & 10 \\ \hline 4 & 8 \\ \hline 6 & 6 \\ \hline 8 & 4 \\ \hline 10 & 2 \\ \hline \end{array} \][/tex]
Step-by-step solution to find the slope:
1. Identify two points on the graph: Let's use the first two points [tex]\((0, 12)\)[/tex] and [tex]\((2, 10)\)[/tex].
2. Calculate the slope [tex]\( m \)[/tex] using the formula for the slope of a line through two points:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1) = (0, 12)\)[/tex] and [tex]\((x_2, y_2) = (2, 10)\)[/tex].
3. Plug in the values:
[tex]\[ m = \frac{10 - 12}{2 - 0} = \frac{-2}{2} = -1 \][/tex]
4. Interpret the slope:
- The slope [tex]\( m = -1 \)[/tex] means the altitude decreases by 1 kilometer for every 1 minute that passes. In other words, the plane descends.
Thus, the practical meaning of the slope is:
[tex]\[ \text{a. For every minute that passes the airplane descends 1 kilometer.} \][/tex]
Therefore, the correct answer is:
a. For every minute that passes the airplane descends 1 kilometer.
