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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See the blue dot in the attached image.
First, find the x value on the coordinate plane. The x value is the first number in the point coordinates, so in this case, it is 4. Move to the right 4. (If it was negative, you would move to the left.)
Then, find the y value, which is the second number of the coordinates. In this case, it is -1, so move down 1. (If it was positive, you’d move up.)
Now, mark this point. This is (4, -1).
First, find the x value on the coordinate plane. The x value is the first number in the point coordinates, so in this case, it is 4. Move to the right 4. (If it was negative, you would move to the left.)
Then, find the y value, which is the second number of the coordinates. In this case, it is -1, so move down 1. (If it was positive, you’d move up.)
Now, mark this point. This is (4, -1).