```Question 120206
First step is to find the required slope value.  Perpendicular lines have slopes that are negative reciprocals of each other:  {{{m[1]=-(1/m[2])}}}

The equation of the perpendicular is {{{2x+7y=16}}}.  Put this into slope-intercept form, {{{y=mx+b}}}, by solving for y.

{{{2x+7y=16}}}
{{{7y=-2x+16}}}
{{{y=((-2)/7)x +16}}}, which tells us that the slope of the perpendicular to the desired line is {{{-(2/7)}}}.

Using {{{m[1]=-(1/m[2])}}}, we now know that the slope of the desired line is {{{7/2}}}.

Now we have a point, (5,-3) and a slope, {{{7/2}}}, so use the point slope form of the line:

{{{(y-y[1])=m(x-x[1])}}} where m is the slope and ({{{x[1]}}},{{{y[1]}}}) are the coordinates of the given point.

{{{y-(-3)=(7/2)(x-5))}}}

Now simplify to standard form:

Multiply by 2

{{{2y+6=7(x-5)}}}

Distribute:

{{{2y+6=7x-35}}}

{{{-7x+2y+6=-35}}}

{{{-7x+2y=-41}}} is the desired equation, though it would be a little tidier to multiply through by -1:

{{{7x-2y=41}}}

{{{graph(600,600,-20,20,-20,20,grid(2),-(2x/7)+16,(7/2)x-(41/2))}}}
Hope this helps,
John

```