Question 1144439
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..., slope-intercept equation for a line passing through the point (4,- 3 )that is parallel to the line 4 x + 5 y = 9....
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Slope needed is {{{-4/5}}}.


{{{y+3=-(4/5)(x-4)}}}
{{{y+3=-4x/5+1}}}
{{{highlight(y=-4x/5-2)}}}


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line passing through the point (4,-3) that is perpendicular to the line 4 x + 5 y=9. 
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Slope to use is  {{{5/4}}}.

You can start with point-slope form  {{{y+3=(5/4)(x-4)}}} and do the algebra steps...

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