To find the equation that describes the relationship between \( x \) and \( y \) based on the given table, we can observe the pattern in the values:
- When \( x = 0 \), \( y = -10 \)
- When \( x = 1 \), \( y = -9 \)
- When \( x = 2 \), \( y = -8 \)
- When \( x = 3 \), \( y = -7 \)
From the pattern, we can see that as \( x \) increases by 1, \( y \) increases by 1 as well. This indicates a linear relationship.
To express this in function notation, we can write the relationship in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- The slope \( m \) is 1 (since \( y \) increases by 1 for each increase of 1 in \( x \)).
- Looking at the table, when \( x = 0 \), \( y = -10 \), which is the y-intercept \( b \).
Putting it all together, the equation that describes the relationship in function notation is:
\[ y = 1x - 10 \]
Or simply:
\[ y = x - 10 \]