Complete the equation of the line through \( (-10,-7) \) and \( (-5,-9) \). Use exact numbers. \( y=\square \)

To find the equation of the line through the points \( (-10,-7) \) and \( (-5,-9) \), we first need to calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-9 - (-7)}{-5 - (-10)} = \frac{-9 + 7}{-5 + 10} = \frac{-2}{5} \] Now we can use the point-slope form of the equation of a line, which is \( y - y_1 = m(x - x_1) \). Using one of the points, let's use \( (-10, -7) \): \[ y - (-7) = -\frac{2}{5}(x - (-10)) \] This simplifies to: \[ y + 7 = -\frac{2}{5}(x + 10) \] Now, distribute and solve for y: \[ y + 7 = -\frac{2}{5}x - 4 \] \[ y = -\frac{2}{5}x - 4 - 7 \] \[ y = -\frac{2}{5}x - 11 \] So, the completed equation of the line is: \[ y = -\frac{2}{5}x - 11 \]