To find the equation that represents the dolphin's elevation [tex]\( y \)[/tex] after [tex]\( x \)[/tex] seconds, let's follow these steps:
1. Determine the initial elevation: The dolphin starts 10 feet below sea level. This gives us an initial elevation of [tex]\(-10\)[/tex] feet.
2. Determine the rate of descent: The dolphin dives at a rate of 9 feet per second. Because it is diving downward, this rate is represented as [tex]\(-9\)[/tex] feet per second.
3. Write the equation: The general form of the linear equation for elevation over time is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the rate of descent (slope) and [tex]\( b \)[/tex] is the initial elevation (y-intercept).
- In this context:
- [tex]\( m \)[/tex] (rate of descent) = [tex]\(-9\)[/tex]
- [tex]\( b \)[/tex] (initial elevation) = [tex]\(-10\)[/tex]
4. Substitute [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the equation:
[tex]\[
y = -9x - 10
\][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B. \ y = -9x -10} \][/tex]
