Question 84357
<pre><font size = 3><b>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 = {{{(-1/5)x + 3/5}}}  divided through by 5
     
     Compare that to

     y = mx + b

m = -1/5, b = {{{3/5}}} 

This means the slope, m, is -1/5, and the y-intercept is (0,{{{3/5}}})
We don't need the y-intercept in this problem, because all 
we need is the slope, which is {{{-1/5}}}.

They are perpendicular because -1/5 is the reciprocal of 5 with the
sign changed.

Edwin</pre>