Question 76628
All you care about is the slopes of the lines.
If the slopes are equal, they are parallel.
If they are perpendicular, they have the relationship
{{{m[1] = - 1/m[2]}}}
First, find the slopes
{{{y - 3x = 10}}}
add 3x to both sides
{{{y = 3x + 10}}}
The form is {{{y = mx + b}}} where m is the slope, so {{{m[1] = 3}}}
-----------------------
{{{3y + x = -5}}}
subtract x from both sides
{{{3y = -x - 5}}}
divide both sides by 3
{{{y = -(1/3)x - 5}}}
so, {{{m[2] = -(1/3)}}}
The relation {{{m[1] = - 1/m[2]}}} is true, so the lines
are perpendicular. All you care about is the numbers in
front of the x.