Question 809479
What is the slope of 7x+8y=2?
Put it into slope-intercept form:
{{{8y=-7x+2}}}
{{{y=-(7/8)x+1/4}}}---------------The equation transformed.  Slope is {{{-(7/8)}}}.


The line perpendicular to that one must have slope {{{+8/7}}}.


Using general form of the slope-intercept form, y=mx+b, solve for b.
{{{b=y-mx}}}.
Now, use your given point, and the found slope, to find the desired line containing the point and perpendicular to {{{y=-(7/8)x+1/4}}}.


That final process:
{{{b=5-(8/7)(-9)}}}
{{{b=5+72/7}}}
{{{b=35/7+72/7}}}
{{{b=107/7}}}
{{{b=15&2/7}}}


In slope-intercept form, you want the equation, {{{highlight(y=(8/7)x+15&2/7)}}}