To determine the equation of the line representing the elevation of the dolphin after \( x \) seconds, we need to consider both the initial condition and the rate of change.
Let's break down the information provided:
1. Initial Elevation:
- The dolphin starts 10 feet below sea level. This means that at \( x = 0 \) seconds, the elevation \( y \) is -10 feet.
2. Rate of Change:
- The dolphin dives at a rate of 9 feet per second. This rate is a constant change in elevation and since it is diving, the elevation decreases with time. Therefore, this rate is negative: -9 feet per second.
Using the slope-intercept form of a linear equation \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y-intercept (initial elevation), we can plug in the given values:
- \( m = -9 \)
- \( b = -10 \)
Thus, the equation becomes:
[tex]\[ y = -9x - 10 \][/tex]
According to the options given:
A. \( y = 9x - 10 \)
B. \( y = -9x - 10 \)
C. \( y = 9x + 10 \)
D. \( y = -9x + 10 \)
The correct equation that represents the dolphin's elevation after \( x \) seconds is:
[tex]\[ \boxed{y = -9x - 10} \][/tex]
