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.

Parallel Perpendicular Neither

-x+4y=8 4x+y=-1 y=-14x+6 y=-4x-3

In order to Check whether a Line is Parallel or Perpendicular we need to check the Slopes of the lines which we are comparing.

If the Slopes of both of these lines are Equal then the lines are Parallel If the Product of the Slopes of these lines is Equal to - 1, then they are Perpendicular.

Given Line is - x + 4y = 20

Writing into slope - intercept form : y = mx + c

⇒ 4y = x + 20

⇒ y = x/4 + 5

Comparing with standard form we can say that slope of this line is 1/4

Now we need to check the slopes of the Given Options to determine whether they are Parallel or Perpendicular or Neither.

1st Line:

⇒ - x + 4y = 8

⇒ 4y = x + 8

⇒ y = x/4 + 2

⇒ Slope of this line is 1/4

As this line Slope is Equal to the Given Line's Slope

⇒ - x + 4y = 8 line is Parallel to - x + 4y = 20

2nd Line:

⇒ 4x + y = - 1

⇒ y = - 1 - 4x

⇒ Slope of this line is - 4

As Product of (1/4) and - 4 is - 1

⇒ 4x + y = - 1 is Perpendicular to the Line - x + 4y = 20

3rd line:

⇒ y = - 14x + 6

⇒ Slope of this line is - 14

As this Line's Slope has no relation with the Slope of the Given line.

y = - 14x + 6 is neither Parallel nor Perpendicular

4th Line:

⇒ y = - 4x - 3

⇒ Slope of this line is - 4

As Product of (1/4) and - 4 is - 1

⇒ y = - 4x - 3 is Perpendicular to the Line - x + 4y = 20