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Determine if the following pairs of lines are parallel, perpendicular, or neither.

2x+2y = 4
2x-2y = 8

User Redzack
by
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1 Answer

6 votes

Answer:

perpendicular

Explanation:

First lets put the two equations in y = mx + b form by solving for y

First equation : 2x + 2y = 4

==> subtract 2x from both sides

2y = 4 - 2x

==> divide both sides by 2

y = 2 - x

==> rearrange terms

y = -x + 2

Second equation 2x - 2y = 8

==> subtract 2x from both sides

-2y = 8 - 2x

==> divide both sides by -2

y = -4 + x

==> rearrange terms

y = x - 4

Now to determine whether the two lines are parallel, perpendicular or neither we look at the slope

If:

  • The slopes are the same then the two lines will never cross and will therefore be parallel (note that they must have different y intercepts)
  • The slopes are reciprocals of each other then they are perpendicular (note that the reciprocal is the inverse of a mathematical term. e.g. the reciprocal of -2 would be 1/2)
  • If neither of these apply to the lines then they are neither

Here, one of the lines has a slope of -1 and the other has a slope of 1. These are reciprocals of each other as the inverse of -1 is 1 vise versa.
So we can say that the lines are perpendicular.

We can also check this by graphing, if the two lines intersect and create 4 90 degree angles then they are perpendicular.

Determine if the following pairs of lines are parallel, perpendicular, or neither-example-1
User Shobhit Sharma
by
4.7k points