Explain in words how to write an equation that is part one: parallel and then also part two: perpendicular to the equation y= 2/3x-4 passing through the point (-2,-5) write your answer in standard form

You are given the line l with equation

1. The equation of line that passes through the point (-2,-5) and is parallel to the line l.

Parallel lines have the same slope. So the slope of unknown line is

Then the equation is

This line passes through point (-2,-5), this means that coordinates of this point satisfy the equation, substitute x=-2 and y=-5 into equation:

Thus, the equation of parallel line is

2. The equation of line that passes through the point (-2,-5) and is perpendicular to the line l.

Perpendicular lines have slopes that satisfy the condition

Therefore, the slope of perpendicular line is

Then the equation is

This line passes through point (-2,-5), this means that coordinates of this point satisfy the equation, substitute x=-2 and y=-5 into equation:

Thus, the equation of perpendicular line is