line includes the points \( (5,-6) \) and \( (-9,-4) \). What is its equation in point-slope form? Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions. Submit

To find the equation of the line in point-slope form, we first need to calculate the slope using the points \( (5, -6) \) and \( (-9, -4) \). The formula for slope \( m \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-6)}{-9 - 5} = \frac{-4 + 6}{-14} = \frac{2}{-14} = -\frac{1}{7} \] Now that we have the slope \( m = -\frac{1}{7} \), we can use one of the points (let's use \( (5, -6) \)) in the point-slope form. The point-slope form of a line is: \[ y - y_1 = m(x - x_1) \] Substituting the values we have: \[ y - (-6) = -\frac{1}{7}(x - 5) \] This simplifies to: \[ y + 6 = -\frac{1}{7}(x - 5) \] So the equation of the line in point-slope form is: \[ y + 6 = -\frac{1}{7}(x - 5) \]