Question

Determine if the lines are parallel, perpendicular, or neither. x - y = 4 and x + y = 9

Answer 1

Answer:

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Answer 2

Answer:

Perpendicular

Step-by-step explanation:

What I would do first is to rearrange these equations into the equation of a line formula: $y=mx+c$

To do so, we isolate y:

x - y = 4 -> -y = -x+4 -> (multiply both sides by -1) y=x-4

x+y=9 -> y=-x+9

We know that in the formula y=mx + c, m stands for gradient of a line (The degree of steepness of the line), and we know that if there is no number before x it means that it is 1 or -1 (depending on the sign before x).

so that on y=x-4 the gradient is 1 and on y=-x+9 the gradient is -1.

We now can check if its parallel, perpendicular or neither with these equations:

m1 · m2 = -1 for perpendicular,   m1 = m2  for parallel,(where m = gradient)

we plug the values of the two gradients into the first equation

(m1 · m2 = -1) and it fits: 1 x -1 = -1

If we plug the same values into the second equation (m1 = m2), we can check that 1 ≠ -1

In conclusion, we can check that these lines are perpendicular to each other.