To find the equation described in the table, we notice that the values of \( y \) seem to be changing in a consistent manner as \( x \) increases.
Looking at the pairs:
- 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. This suggests a linear relationship.
The slope \( m \) of the function can be identified as \( 1 \), where: \[ m = \frac{\Delta y}{\Delta x} = \frac{-9 - (-10)}{1 - 0} = 1 \]
The y-intercept \( b \) is the value of \( y \) when \( x = 0 \), which is \(-10\).
Thus, we can write the equation in slope-intercept form \( y = mx + b \): \[ y = 1x - 10 \]
In function notation, this can be written as: \[ f(x) = 1x - 10 \]
Simplifying, we get: \[ f(x) = x - 10 \]
So, the final answer is: \[ f(x) = x - 10 \]