Question 157214
{{{x+y=10}}}
{{{y=-x+10}}}
The slope of that line is {{{m[1]=-1}}}.
Parallel lines have identical slopes.
{{{m[1]=m[2]=-1}}}
Use the point-slope form of a line.
{{{y-y[p]=m(x-x[p])}}}
The origin is 
{{{x[p]=y[p]=0}}}
Substituting all the values. 
{{{y-y[p]=m(x-x[p])}}}
{{{y-0=(-1)(x-0)}}}
{{{y=-x}}}
Graph them to prove out the solution.
{{{ graph( 300, 300, -5, 5, -3, 12, -x+10, -x) }}}