Consider the line y=(4)/(3)x+8 Find the equation of the line that is parallel to this line and passes through the point (-8,2) Find the equation of the line that is perpendicular to this line and passes through the point (-8,2) Equation of parallel line: Equation of perpendicular line: square

To find the equation of the line that is parallel to the given line and passes through the point , we need to use the fact that parallel lines have the same slope.Step 1: Identify the slope of the given line.The slope of the given line is .Step 2: Use the point-slope form of a linear equation to find the equation of the parallel line.The point-slope form of a linear equation is , where is a point on the line and is the slope.Substituting the values, we have: Step 3: Simplify the equation. Therefore, the equation of the line that is parallel to the given line and passes through the point is .To find the equation of the line that is perpendicular to the given line and passes through the point , we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.Step 1: Find the negative reciprocal of the slope of the given line.The negative reciprocal of is .Step 2: Use the point-slope form of a linear equation to find the equation of the perpendicular line.Using the point-slope form again, we have: Step 3: Simplify the equation. Therefore, the equation of the line that is perpendicular to the given line and passes through the point is .