Question 113465
Parallel lines have slopes that are equal, and perpendicular lines have slopes that are the negative reciprocal of each other {{{m[1]=(-1)/m[2]}}}.


Now the problem is to find the slope on each of the two lines and compare them.  The equations are currently in standard form, so we need to convert them to slope-intercept form.  The slope-intercept form is {{{y=mx+b}}} where m is the slope.  All that needs to be done is rearrange the equations so they have y on the left and everything else on the right.


{{{x-6y=24}}}
{{{-6y=-x+24}}}  Add -x to both sides
{{{y=(1/6)x-4}}}  Divide both sides by -6


Now we know the slope of the first line is {{{m[1]=1/6}}}


Let's do the second one the same way.


{{{6x+y=6}}}
{{{y=-6x+6}}} A -6x to both sides

Now we know the slope of the second line is {{{m[2]=-6}}}


Comparing them we see that {{{m[1]=-(1/m[2])}}}, therefore the lines are perpendicular.


Hope this helps,
John