To find the equation of the perpendicular line, we can use the fact that the slopes of perpendicular lines are negative reciprocals. The slope of the given line is -6/5, so the slope of the perpendicular line is 5/6.
Using the point-slope form of a linear equation, we can write the equation of the perpendicular line as:
y - (-4) = (5/6)(x - (-6))
Simplifying this equation, we get:
y = 5x/6 + 24/6
y = 5x/6 + 4
To find the equation of the parallel line, we can use the fact that the slopes of parallel lines are equal. The slope of the given line is -6/5, so the slope of the parallel line is also -6/5.
Using the point-slope form of a linear equation, we can write the equation of the parallel line as:
y - (-4) = (-6/5)(x - (-6))
Simplifying this equation, we get:
y = -6x/5 + 24/5
y = -6x/5 + 4
Therefore, the equation of the perpendicular line is y = 5x/6 + 4, and the equation of the parallel line is y = -6x/5 + 4.
