To determine the correct statement about the slope of the linear function based on the given data points, let's follow these detailed steps:
1. Identify the Data Points:
We are given the following data points for minutes ([tex]\(x\)[/tex]) and altitude ([tex]\(y\)[/tex]):
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Minutes, } x & \text{Altitude in feet, } y \\
\hline
15 & 22,500 \\
\hline
20 & 20,000 \\
\hline
25 & 17,500 \\
\hline
30 & 15,000 \\
\hline
\end{array}
\][/tex]
2. Select Data Points to Calculate Slope:
We need two points to calculate the slope of the linear function. Let's choose the points [tex]\((15, 22,500)\)[/tex] and [tex]\((30, 15,000)\)[/tex].
3. Calculate the Slope:
The slope [tex]\(m\)[/tex] of a line through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in the points [tex]\((15, 22,500)\)[/tex] and [tex]\((30, 15,000)\)[/tex]:
[tex]\[
m = \frac{15,000 - 22,500}{30 - 15}
\][/tex]
[tex]\[
m = \frac{-7,500}{15}
\][/tex]
[tex]\[
m = -500
\][/tex]
4. Interpret the Slope:
The slope is [tex]\(-500\)[/tex]. A negative slope indicates that as the minutes increase, the altitude decreases. Hence, the rate of change is negative.
5. Determine the Correct Statement:
Based on the interpretation of the negative slope:
- The slope is not positive.
- As the minutes ( [tex]\(x\)[/tex] ) increase, the altitude ([tex]\( y \)[/tex]) decreases.
Therefore, the correct statement is:
The slope is negative because as the minutes increase, the altitude decreases.
