Consider the line y = -8x+
find the equation of the line that is perpendicular to this line and passes through the point (-4, 4).
find the equation of the line that is parallel to this line and passes through the point (-4, 4).
equation of perpendicular line:
equation of parallel line:

Part 1) The equation of the perpendicular line is  

Part 2) The equation of the parallel line is

Step-by-step explanation:

Part 1) Find the equation of the line that is perpendicular to the given line and passes through the point (-4, 4)

The slope of the given line is

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

so

The slope of the line perpendicular to the given line is

Find the equation of the perpendicular line in point slope form

we have

substitute

Convert to slope intercept form

isolate the variable y

apply distributive property right side

Part 2) Find the equation of the line that is parallel to the given line and passes through the point (-4, 4)

The slope of the given line is

Remember that

If two lines are parallel, then their slopes are the same

so

The slope of the line parallel to the given line is

Find the equation of the parallel line in point slope form

we have

substitute

Convert to slope intercept form

isolate the variable y

apply distributive property right side

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.