Answer:
perpendicular
Step-by-step 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.
