Question 275632
The equation is in the "standard form"
You need to get it in the "slope-intercept" form
which is:
{{{y = mx + b}}}
In this form, {{{m}}} is the slope
{{{5x -2y = 12}}}
Subtract {{{5x}}} from both sides
{{{-2y = -5x + 12}}}
Divide both sides by {{{-2}}}
{{{y = (5/2)*x - 6}}}
Now it is in the slope-intercept form
where {{{m = 5/2}}}
The rule is, that any line perpendicular to this line will have 
slope = {{{-(1/m)}}}
{{{-(1/m) = -(1/(5/2))}}}
{{{-(1/(5/2)) = -(2/5)}}}
The slope of any line perpendicular to {{{5x - 2y = 12}}}
is {{{-(2/5)}}}