Question 373190
Since the inequality does not contain an "=" portion, then the boundary line will be dotted to signify that it is not included in the solution.
Plot the line,
{{{5x+10y=0}}}
{{{10y=-5x}}}
{{{y=-(1/2)x}}}
.
.
.
{{{graph(300,300,-10,10,-10,10,0,-(1/2)x)}}}
.
.
.
Now choose a point not on the line. 
({{{2}}},{{{2}}}) is a convenient choice.
Test the inequality.
If the inequality is satisfied, shade the region containing ({{{2}}},{{{2}}}).
If not, shade the region that does not contain ({{{2}}},{{{2}}}).
{{{5x+10y>0}}}
{{{5(2)+10(2)>0}}}
{{{10+20>0}}}
{{{30>0}}}

True, shade the region containing ({{{2}},{{{2}}})

*[invoke plot_any_inequality "5x+10y>0", -10, 10, -10, 10, 300, 300]