To convert the arithmetic sequence given by the formula \( a_n = 13 + (n-1)(-2) \) into a linear function equation, we can simplify the expression:
- Start with the original sequence formula: \[ a_n = 13 + (n-1)(-2) \]
- Distribute \((-2)\) across \((n-1)\): \[ a_n = 13 - 2(n-1) = 13 - 2n + 2 \]
- Combine like terms: \[ a_n = 15 - 2n \]
To express this in the form \(y = mx + b\), where \(y\) corresponds to \(a_n\) and \(x\) corresponds to \(n\), we can rewrite it as: \[ y = -2n + 15 \]
This means the correct equation for the linear function is: \[ y = -2x + 15 \]
Therefore, the correct response is: y = −2x + 15 (y is equal to negative 2 x plus 15).