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.
<u>1st Line : </u>
⇒ -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
<u>2nd Line :</u>
⇒ 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
<u>3rd line :</u>
⇒ 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
<u>4th Line :</u>
⇒ 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
