Question 324964
Find the slope of the line by putting it into slope-intercept form, {{{y=mx+b}}}
{{{9x+8y=5}}}
{{{8y=-9x+5}}}
{{{y=-(9/8)x+5/8}}}
Perpendicular lines have slopes that are negative reciprocals,
{{{m1*m2=-1}}}
{{{-(9/8)*m2+-1}}}
{{{m2=8/9}}}
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The new line will have the equation,
{{{y=(8/9)x+b}}} Use the point (0,-7) to solve for b.
{{{-7=(8/9)(0)+b}}}
{{{b=-7}}}
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{{{highlight(y=(8/9)x-7)}}}
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{{{drawing(300,300,-8,8,-8,8,grid(1),circle(0,-7,.3),graph(300,300,-8,8,-8,8,-(9/8)x+5/8,(8/9)x-7))}}}