To find the equation described in the given table, we observe the relationship between \( x \) and \( y \).
The values in the table are:
- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)
We can see that as \( x \) increases by 1, \( y \) increases by 1 as well. This indicates that the function has a slope of 1.
Let's establish the function in the form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Slope (m): From the observations, \( m = 1 \).
- Y-intercept (b): When \( x = 0 \), \( y = -10\), therefore \( b = -10 \).
Combining these, we get the function in the form:
\[ f(x) = 1x - 10 \]
We can simplify that to:
\[ f(x) = x - 10 \]
So the equation described in the table is:
\[ f(x) = x - 10 \]