Find an equation for the line that passes through the points \( (-4,4) \) and \( (6,-4) \).

To find the equation of the line that passes through the points \((-4, 4)\) and \((6, -4)\), we first calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 4}{6 - (-4)} = \frac{-8}{10} = -\frac{4}{5} \] Now that we have the slope, we can use the point-slope form of the line's equation, which is \(y - y_1 = m(x - x_1)\). Using the point \((-4, 4)\): \[ y - 4 = -\frac{4}{5}(x + 4) \] To simplify, distribute the slope: \[ y - 4 = -\frac{4}{5}x - \frac{16}{5} \] Now, add \(4\) (or \(\frac{20}{5}\)) to both sides: \[ y = -\frac{4}{5}x + \frac{4}{5} \] So, the equation of the line is: \[ y = -\frac{4}{5}x + \frac{4}{5} \]