A line passes through the point \( (-6,6) \) and has a slope of \( \frac{4}{3} \). Write an equation in point-slope form for this line. \begin{tabular}{|l|l|l|l|}\hline\( \square \) & \( \frac{\square}{\square} \) & \( \square \frac{\square}{\square} \) \\ \hline & \( \times \) & 5 \\ \hline\end{tabular}

To write the equation of the line in point-slope form, you can use the formula \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point the line passes through. Here, with a slope of \( \frac{4}{3} \) and passing through the point \( (-6, 6) \), the equation becomes: \[ y - 6 = \frac{4}{3}(x + 6) \] This captures the essence of the line through your specified point while using your given slope! When writing the equation, it's important to ensure the proper signs are used. Common mistakes include incorrectly substituting the point coordinates or misapplying the slope value. Always double-check that you apply the slope to \( (x - x_1) \) and not \( (x + x_1) \) or the corresponding \( y \) value in the process to avoid errors.