Is each line parallel, perpendicular, or neither parallel nor perpendicular to the line −x+4y=20?

drag each choice into the boxes to correctly complete the table.

we have

Isolate the variable y

the slope m of the given line is

we know that

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

so

if two lines are perpendicular, then the product of their slopes is equal to minus one

so

we will proceed to verify each case to determine the solution

case A)

Isolate the variable y

the slope  is

Compare the slope of the line of the case A) with the slope of the given line

 -----> slope given line

----> slope line case A)

--------> the lines are parallel

case B)

Isolate the variable y

the slope  is

Compare the slope of the line of the case B) with the slope of the given line

 -----> slope given line

----> slope line case B)

--------> the lines are perpendicular

case C)

the slope  is

Compare the slope of the line of the case C) with the slope of the given line

 -----> slope given line

----> slope line case C)

therefore

the line case C) and the given line are neither parallel nor perpendicular

case D)

the slope  is

Compare the slope of the line of the case D) with the slope of the given line

 -----> slope given line

----> slope line case D)

--------> the lines are perpendicular

the answer in the attached figure

include a picture of the drawing in order for me to

step-by-step explanation:

1. sometimes

2. never true

3. sometimes

step-by-step explanation:

these are pretty self explanatory if you know what supp right and com angles are