Question 117454
First, you have to find the slope of your first line, x+2y=10.
You need to go to slope-intercept form.
{{{x+2y=10}}}
{{{2y=-x+10}}}
{{{y=-(1/2)x+5}}}
{{{drawing( 300, 300, -5, 10, -5, 10,graph( 300, 300, -5, 10, -5, 10, -.5x+5),grid( 1 ))}}}
Now you know the slope of your first line is -1/2.
Then use the point slope form of a line to get the equation of the second line. 
Perpendicular lines have slopes that have a particular relationship.
That is, their slopes are negative reciprocals.
{{{m[2]=-1/m[1]}}}
The slope of your second line is then,
{{{m[2]=-1/(-1/2)}}}
{{{m[2]=2}}}
Now use the point-slope form and substitute,
{{{y-y[1]=m(x-x[1])}}}
where 
{{{x[1]=1}}} and {{{y[1]=1}}}
{{{y-1=2(x-1)}}}
{{{y-1=2x-2}}}
{{{highlight(y=2x-1)}}}
{{{drawing( 300, 300, -5, 10, -5, 10,graph( 300, 300, -5, 10, -5, 10, -.5x+5, 2x-1),grid( 1 ),circle( 1, 1, .2 ))}}}