Verify if the lines 2x-y+2=0 and x+y-4=0 are perpendicular.
Given the lines:
2x-y +2 = 0
x+y -4 = 0
We need to verify if the lines are perpendicular.
We will use the slope to verify.
If the product of the slopes is -1, then the lines are perpendicular.
First we will rewrite the lines into the slope form y=mx+b
==> 2x-y +2 = 0 ==> y= 2x+2 ==> the slope m1 = 2
==> x+y -4 = 0 ==> y= -x + 4 ==> the slope m2 = -1
==> m1*m2 = -2.
Then the lines are not perpendicular.
For the given lines , 2x-y+2=0 and x+y-4=0, we first find their slope.
2x - y + 2 = 0
=> -y = -2x - 2
=> y = 2x + 2
This is in the form y = mx + c , where m is the slope of the line.
So the slope is m1 = 2
For x + y - 4 = 0
=> y = -x + 4
Here the slope is m2 = -1.
Now the slope of two perpendicular lines when multiplied gives the result -1.
As m1*m2 = 2 * -1 = -2 and not -1, we cannot say that the lines are perpendicular.
We'll put both given lines in the point slope form:
y = mx + n, where m is the slope and n is y intercept.
y = 2x + 2
y = -x + 4
If 2 lines are perpendicular, the product of their slopes is -1.
Comparing the given lines with the point slope form of the line, we'll gather the facts that m1 = 2 and m2 = -1.
We'll multiply m1 by m2 and we'll get:
2*(-1) = -2
Since the result is different from -1, then the lines are not perpendicular.
Two lines y = m1*x+c and y = m2*x+d are perpendicular if m1*m2 = -1.
We convert the given two lines in the form y = mx+c
The given 2x-y+2 = 0 could be written as y = 2x+2 ...(1). So slope m1 = 2.
x+y-4 = 0 could be written as: y = -x+4....(2). The slope m2 = -1.
We can see that the product of the slopes m1*m2 = 2*-1 = -2. Since the product of slopes m1*m2 is not equal to zero, we conclude that the given lines are not perpendicular.