To determine the equation described in the table, let's analyze the given values of \(x\) and \(y\):
| \(x\) | \(y\) | |-------|-------| | 0 | -10 | | 1 | -9 | | 2 | -8 | | 3 | -7 |
From the table, we can observe that as \(x\) increases by 1, \(y\) increases by 1 as well. This indicates a linear relationship between \(x\) and \(y\).
Let's express \(y\) in terms of \(x\):
- When \(x = 0\), \(y = -10\)
- When \(x = 1\), \(y = -9\)
- When \(x = 2\), \(y = -8\)
- When \(x = 3\), \(y = -7\)
This suggests a pattern where \(y\) could be represented as a linear function.
To find the equation, we can assume the following linear form: \[ y = mx + b \] where \(m\) is the slope and \(b\) is the y-intercept.
From the table data:
- The slope \(m\) can be determined as \(1\) because for every increase of \(1\) in \(x\), \(y\) increases by \(1\).
- The y-intercept \(b\) can be seen when \(x = 0\): \(y = -10\).
Therefore, the equation can be written as: \[ y = 1x - 10 \] or simply: \[ y = x - 10 \]
Using function notation, we can write this as: \[ f(x) = x - 10 \]
In conclusion, the equation described in the table is: \[ f(x) = x - 10 \]
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