Question 58184
Are the following lines parallel, perpendicular, or neither?   L1 with equation x – 5y = 10   L2 with equation 5x + y = 5
:
Put both equations in slope intercept form so that we can find the slope of each line.  Slope intercept form is:{{{highlight(y=mx+b)}}}, slope=m and (0,b) is the y-intercept.
L1) x-5y=10
{{{-x+x-5y=-x+10}}}
{{{-5y=-x+10}}}
{{{-5y/-5=-x/-5+10/-5}}}
{{{y=(1/5)x-2}}}  slope=m=(1/5)
L2)5x+y=5
{{{-5x+5x+y=-5x+5}}}
{{{y=-5x+5}}}  slope=m=-5 or -5/1
:
Parrallel lines have = slopes.
Perpendiculare lines have slope that are negative reciprocals of each other (opposite signs and upsides down.)
If they're neither of those it's neither.
{{{1/5}}} and {{{-5/1}}} are opposite signs and upside down.  Therefore the lines are parallel.
Happy Calculating!!!