Question 84357: Determine whether each pair of lines is parallel, perpendicular, or neither.
5x-y=8 and 5y= -x+3
Found 2 solutions by funmath, Edwin McCravy:
Answer by funmath(2933)   (Show Source):
You can put this solution on YOUR website! Determine whether each pair of lines is parallel, perpendicular, or neither.
5x-y=8 and 5y= -x+3
If lines are parallel, they have the same slopes. m1=m2
If lines are perpendicular, they have slopes that are negative reciprocals of each other. m1=-1/m2
If the slopes are equal or negative reciprocals they are neither parallel nor perpendicular.
:
To find the slope of an equation of a line, put the equation in slope intercept form: y=mx+b m=slope.
5x-y=8
-5x+5x-y=-5x+8
-y=-5x+8
-(-y)=-(-5x+8)
y=5x-8 the slope of this line is m=5 or m=5/1
5y=-x+3
5y/5=-x/5+3/5
y=(-1/5)x+3/5 the slope of this line is m=-1/5
The slopes of the lines are negative reciprocals of each other (opposite signs and upside down), therefore the lines are perpendicular.
Happy Calculating!!!
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website! Determine whether each pair of lines is parallel,
perpendicular, or neither.
5x-y=8 and 5y= -x+3
If their slopes are equal they are parallel
If the slopes of one is the reciprocal of the slope of the
other with the sign changed, they are perpendicular.
Solve each for y to get them into the slopeintercept form:
Solving the first one for y
5x - y = 8
-y = -5x + 8 (added -5x to both sides
y = 5x - 8 {divided through by -1
Compare that to
y = mx + b
m = 5, b = -8
This means the slope, m, is 5, and the y-intercept is (0,-8)
We don't need the y-intercept in this problem, because all
we need is the slope, which is 5.
Solving the second one for y
5y = -x + 3
y =  divided through by 5
Compare that to
y = mx + b
m = -1/5, b = 
This means the slope, m, is -1/5, and the y-intercept is (0,)
We don't need the y-intercept in this problem, because all
we need is the slope, which is  .
They are perpendicular because -1/5 is the reciprocal of 5 with the
sign changed.
Edwin
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