Write an equation of the line passing through the points \( (4,11) \) and \( (-2,-19) \). The equation of the line is \( \square \). (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

To find the equation of the line passing through the points \( (4, 11) \) and \( (-2, -19) \) in slope-intercept form \( y = mx + b \), follow these steps: 1. **Calculate the slope \( m \):** \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-19 - 11}{-2 - 4} = \frac{-30}{-6} = 5 \] 2. **Find the y-intercept \( b \):** Use one of the points to solve for \( b \). Let's use \( (4, 11) \): \[ 11 = 5(4) + b \\ 11 = 20 + b \\ b = 11 - 20 \\ b = -9 \] 3. **Write the equation of the line:** \[ y = 5x - 9 \] **Final Answer:** \[ y = 5x - 9 \]