Question 241609
The rule is: if you have a line with slope = {{{m}}}, then
ANY line perpendicular to it will have slope = {{{-(1/m)}}}
So, first you have to find the slope of your line.
Get it into the form {{{y = mx + b}}} where {{{m}}} = slope
{{{7x + 9y = -25}}}
{{{9y = -7x - 25}}}
{{{y = -(7/9)*x - 25/9}}}
You can see that {{{m = -(7/9)}}}
Now you have to find {{{-(1/m)}}}
Divide both sides by {{{m}}}
{{{1 = -(7/9)*(1/m)}}}
Divide both sides by {{{7/9}}}
{{{1/(7/9) = -(1/m)}}}
{{{9/7 = -(1/m)}}}
So, ANY line perpendicular to the given line will have this slope
The line you're looking for passes through (8,-9)
The formula is
{{{(y - y[1])/(x -x[1]) = m}}} where( {{{x[1]}}}, {{{y[1]}}}) is the given point
{{{(y - (-9))/(x - 8) = 9/7}}}
Multiply both sides by {{{x-8}}}
{{{y + 9 = (9/7)*(x-8)}}}
{{{y + 9 = (9/7)*x - 72/7}}}
{{{y = (9/7)*x - 63/7 - 72/7}}}
{{{y = (9/7)*x - 135/7}}} answer
Or, if you like,
{{{9x - 7y - 135 = 0}}}
I'll plot both lines
{{{ graph( 600, 600, -20, 25, -20, 25, -(7/9)*x - 25/9, (9/7)*x - 135/7) }}}