are these two lines perpendicular?
x+2y=5
2x+4y=7
How do I determine if these two are perpendicular?
it is not perpendicular is this correct?
Correct!
Perpendicular lines have slopes that are negative reciprocals of each other.
Thus perpendiculars of
y = -(1/2)x + anything
will have a form like
y = 2 + something
The two lines you specified are in fact parallel, because they have the same slope : (y = -x/2 + something)
thanks Jim
To determine if two lines are perpendicular, you need to compare their slopes. If the slopes of the two lines are negative reciprocals of each other, then they are perpendicular.
To determine the slope of each line, you can rearrange the equations into the slope-intercept form: y = mx + b, where m represents the slope.
Let's start with the first equation: x + 2y = 5.
Rearranging the equation, we get:
2y = -x + 5
Divide the entire equation by 2:
y = -1/2x + 5/2
By comparing the rearranged equation to y = mx + b, we can see that the slope (m) of the first line is -1/2.
Now, let's look at the second equation: 2x + 4y = 7.
Rearranging the equation, we get:
4y = -2x + 7
Divide the entire equation by 4:
y = -1/2x + 7/4
Comparing this equation to y = mx + b, we can see that the slope (m) of the second line is also -1/2.
Since the slopes of both lines are equal, -1/2, and not negative reciprocals of each other, these lines are not perpendicular to each other.