Slope intercept form is y=mx+c
where m is slope and c is y-intercept.
Given equation is x+2y=9. This equation can be written as
y= -x/2 + 9/2
and by comparing it with y=m1x+c
we can find m1=-1/2
Now we have to find slope-intercept form of equation passing through (2,8).
slope of the line passing through (2,8) and perpendicular to the given line can be calculated as
m1*m2=-1 where as m1 is the slope of given line and m2 is the slope of line passing through (2,8) and perpendicular to the given line.
-1/2 x m2=-1
using general equation
y=mx+c which can be written as y=m2x+c
we have now m2=2 and one pair (x,y)= (2,8). We can calcuate c.
Therefore required equation is
y=2x+4 (m2=2 and c=4 for required line).