Complete the equation of the line through \( (6,-6) \) and \( (8,8) \). Use exact numbers. \( y=\square \)

To find the equation of the line through the points \( (6, -6) \) and \( (8, 8) \), we first need to determine the slope (m) of the line using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in the coordinates, we get: \( m = \frac{8 - (-6)}{8 - 6} = \frac{8 + 6}{2} = \frac{14}{2} = 7 \). With the slope of the line known, we can use the point-slope form of the equation of a line \( y - y_1 = m(x - x_1) \). Using point \( (6,-6) \), we substitute: \( y - (-6) = 7(x - 6) \) Simplifying gives: \( y + 6 = 7x - 42 \) Thus, the equation becomes: \( y = 7x - 48 \). So the completed equation of the line is \( y = 7x - 48 \). Happy calculating!