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.

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

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