To find the equation representing the bottlenose dolphin's elevation [tex]\( y \)[/tex] after [tex]\( x \)[/tex] seconds, you need to consider its initial elevation and how the elevation changes over time.
1. Initial Elevation:
The dolphin starts at [tex]\( 10 \)[/tex] feet below sea level, which is represented by [tex]\( -10 \)[/tex] feet.
2. Rate of Dive:
The dolphin dives at a rate of [tex]\( 9 \)[/tex] feet per second. Because it is diving (going down), this rate is [tex]\( -9 \)[/tex] feet per second.
3. General Form of the Linear Equation:
The general form of a linear equation is:
[tex]\[
y = mx + b
\][/tex]
Here, [tex]\( m \)[/tex] is the slope (rate of change) and [tex]\( b \)[/tex] is the y-intercept (initial value).
4. Applying Values:
- The slope [tex]\( m \)[/tex] is [tex]\(-9\)[/tex] because the dolphin dives at a rate of [tex]\( -9 \)[/tex] feet per second.
- The y-intercept [tex]\( b \)[/tex] is [tex]\(-10\)[/tex] because the initial elevation is [tex]\( 10 \)[/tex] feet below sea level.
Thus, substituting these values into the equation, we get:
[tex]\[
y = -9x - 10
\][/tex]
So the correct equation that represents the dolphin’s elevation after [tex]\( x \)[/tex] seconds is:
[tex]\[
\boxed{y = -9x - 10}
\][/tex]
This corresponds to choice B.
