Question 145481
First get the equation in the form
{{{y = mx + b}}}
where m is the slope, then the line perpendicular
to it will have slope = {{{m[1] = -(1/m)}}}
{{{x + 3y = 12}}}
subtract {{{x}}} from both sides
{{{3y = -x + 12}}}
divide both sides by {{{3}}}
{{{y = -(1/3)x + 4}}}
{{{m[1] = -(1/m)}}}
{{{m[1] = -(1/(-1/3))}}}
{{{m[1] = 3}}}
So the line perpendicular to the given line will look like
{{{y = 3x + b}}}
To find {{{b}}}, plug (9, -5) into the equation
{{{-5 = 3*9 + b}}}
{{{-5 - 27 = b}}}
{{{b = -32}}}
The answer is {{{y = 3x - 32}}}
check:
does it go through (9, -5)?
{{{-5 = 3*9 - 32}}}
{{{-5 = 27 - 32}}}
{{{-5 = -5}}}
OK