4. \( (0,-8) \) and \( (3,2) \)

It seems like you have provided two points: \( (0, -8) \) and \( (3, 2) \). If you would like to find the equation of the line that passes through these two points, we can do that using the slope-intercept form of a line. 1. **Calculate the slope (m)**: The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points \( (0, -8) \) and \( (3, 2) \): \[ m = \frac{2 - (-8)}{3 - 0} = \frac{2 + 8}{3} = \frac{10}{3} \] 2. **Use the point-slope form to find the equation**: The point-slope form of a line is given by: \[ y - y_1 = m(x - x_1) \] Using point \( (0, -8) \) and the slope \( \frac{10}{3} \): \[ y - (-8) = \frac{10}{3}(x - 0) \] Simplifying this: \[ y + 8 = \frac{10}{3}x \] \[ y = \frac{10}{3}x - 8 \] 3. **Convert to slope-intercept form**: The equation of the line in slope-intercept form is: \[ y = \frac{10}{3}x - 8 \] So, the equation of the line that passes through the points \( (0, -8) \) and \( (3, 2) \) is: \[ y = \frac{10}{3}x - 8 \] If you need any further calculations or information, feel free to ask!