Question 1003061

 the graphs of {{{6y=-2x+4}}} and {{{2y=ax-5}}} will be perpendicular if their slopes are negative reciprocals to each other

so, write first  equations in the slope-intercept form

{{{6y=-2x+4}}} 
{{{y=-(2/6)x+4/6}}} 
{{{y=-(1/3)x+2/3}}} 

as you can see, the slope is {{{m=-(1/3)}}}

now to find the slope of the perpendicular line {{{m[p]}}}, find negative reciprocal of {{{m}}} which will be {{{m[p]=-1/m}}}

plug in  {{{-(1/3)}}} for  {{{m}}}

{{{m[p]=-1/(-1/3)}}}

{{{m[p]=3}}}

so, your perpendicular line is:
 
{{{2y=3x-5}}}

see it on a graph:


{{{ graph( 600, 600, -10, 10, -10, 10, -(1/3)x+2/3,3x/2-5/2) }}}