Determine if the lines are parallel, perpendicular, or neither. x - y = 4 and x + y = 9
2 answers:
Answer:
Perpendicular
Step-by-step explanation:
What I would do first is to rearrange these equations into the equation of a line formula:
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.
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