To find the equation described in the table, we first notice the change in y values corresponding to the change in x values.
The table data is:
- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)
As \( x \) increases by 1, \( y \) increases by 1. This indicates a linear relationship with a slope of 1.
Now let's express this relationship in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
From the table:
- The slope \( m = 1 \).
- The y-intercept (when \( x = 0 \)) is \( b = -10 \).
So, the equation is: \[ y = 1x - 10 \] In function notation, we can write: \[ f(x) = x - 10 \]
Thus, the equation described in the table is: \[ f(x) = x - 10 \]