Determine the equation of the line that passes through the points \( (2,-14) \) an \( (8,-68) \). Enter your equation in the form \( y=m x+b \), Simplify your answer completely.

To determine the equation of the line passing through the points \( (2, -14) \) and \( (8, -68) \) in the form \( y = mx + b \), follow these steps: 1. **Calculate the slope (\( m \))**: The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Plugging in the given points: \[ m = \frac{-68 - (-14)}{8 - 2} = \frac{-68 + 14}{6} = \frac{-54}{6} = -9 \] 2. **Determine the y-intercept (\( b \))**: Using the slope-intercept form \( y = mx + b \) and one of the points, say \( (2, -14) \): \[ -14 = (-9)(2) + b \] \[ -14 = -18 + b \] \[ b = -14 + 18 = 4 \] 3. **Write the equation of the line**: Substitute \( m = -9 \) and \( b = 4 \) into the slope-intercept form: \[ y = -9x + 4 \] **Final Answer:** \[ y = -9x + 4 \]