Find an equation of the line passing through the given points. Use function notation to write the equation. \[ (-6,-3) \text { and }(-9,-4) \]

To find the equation of the line passing through the points \((-6, -3)\) and \((-9, -4)\), we can follow these steps: 1. **Calculate the slope (m)** of the line using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \((x_1, y_1) = (-6, -3)\) and \((x_2, y_2) = (-9, -4)\). Substituting the values: \[ m = \frac{-4 - (-3)}{-9 - (-6)} = \frac{-4 + 3}{-9 + 6} = \frac{-1}{-3} = \frac{1}{3} \] 2. **Use the point-slope form of the equation of a line**, which is: \[ y - y_1 = m(x - x_1) \] We can use either of the two points. Let's use \((-6, -3)\): \[ y - (-3) = \frac{1}{3}(x - (-6)) \] Simplifying this: \[ y + 3 = \frac{1}{3}(x + 6) \] 3. **Distribute the slope**: \[ y + 3 = \frac{1}{3}x + 2 \] 4. **Isolate y**: \[ y = \frac{1}{3}x + 2 - 3 \] \[ y = \frac{1}{3}x - 1 \] 5. **Write the equation in function notation**: \[ f(x) = \frac{1}{3}x - 1 \] Thus, the equation of the line passing through the points \((-6, -3)\) and \((-9, -4)\) in function notation is: \[ f(x) = \frac{1}{3}x - 1 \]