Determine if these problems x+2y=5 and -2x+y=5 are parallel, perpendicular, or neither? Thank you
To determine if two lines are parallel, perpendicular or neither we need to compare the value of their slopes. This requires that we put the equations in the general format of a line y = mx + b.
We can rearrange the first equation
x + 2y = 5
by subtracting x from both sides and then dividing by two to get
y = -(1/2) x + 5/2
so the slope of the line is -1/2 and the y-intercept is 5/2.
For the second equation, we rearrange
-2x + y = 5
by adding 2x to both sides of the equation resulting in
y = 2x + 5
This line has a slope of 2 and a y-intercept of 5.
Perpendicular lines have slopes that are the negative reciprocal of each other. The negative reciprocal of 2 is -1/2, so these lines are perpendicular.