Find the equation of the line that is perpendicular to this line and passes through the point \( (-5,6) \). Find the equation of the line that is parallel to this line and passes through the point \( (-5,6) \).

To find the equations of the lines, we first need to determine the slope of the original line. If the equation of the original line is in the form \( y = mx + b \), the slope \( m \) can be used to find both the perpendicular and parallel lines. The slope of a line perpendicular to the original line is the negative reciprocal of \( m \). If \( m \) is the slope of the original line, then the perpendicular line will have a slope of \( -\frac{1}{m} \). Using the point \( (-5,6) \), we can apply the point-slope form \( y - y_1 = m(x - x_1) \). Substituting the values, we can derive the equation for the perpendicular line. For the parallel line, it will share the same slope \( m \) as the original line. Thus, using the same point \( (-5,6) \) and the slope \( m \), we can again utilize the point-slope form to find this line's equation. Once calculated, these equations will uniquely describe the lines with the desired orientations through the specified point!