Consider the line \( y=-9 x+6 \) Find the equation of the line that is parallel to this line and passes through the point \( (-2,6) \). Find the equation of the line that is perpendicular to this line and passes through the point \( (-2,6) \). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of parallel line: Equation of perpendicular line:

Since the given line has a slope of \(-9\), any line parallel to it will also have a slope of \(-9\). Using the point-slope form of a line, we have: \[y - 6 = -9(x + 2)\] Simplifying, we get: \[y = -9x - 12\] Therefore, the equation of the parallel line is \(y = -9x - 12\). Since the given line has a slope of \(-9\), any line perpendicular to it will have a slope of \(\frac{1}{9}\) (the negative reciprocal of \(-9\)). Using the point-slope form of a line, we have: \[y - 6 = \frac{1}{9}(x + 2)\] Simplifying, we get: \[y = \frac{1}{9}x + \frac{52}{9}\] Therefore, the equation of the perpendicular line is \(y = \frac{1}{9}x + \frac{52}{9}\).