Question 188058
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We'll see the Slope of line <font color=blue>-5x-4y=6</font> via Slope-Intercept Form, {{{y=mx+b}}}:
Arranging the variables, 
{{{4y=-5x-6}}}, divide by 4
{{{y=(-5x-6)/4}}}===> {{{y=(-5/4)x-(6/4)}}} ===>{{{y=highlight((-5/4))x-3/2}}}
It's Slope=m1=<font color = blue> -5/4 </font>


*Remember, for perpendicular lines, {{{m[2]=-1/m[1]=(-1)/(-5/4)=(-1)(-4/5)=red(4/5)}}}


The, line passing thru point (-6,6) has slope=m2=4/5, and via Slope-Intercept Form:
{{{6=(4/5)(-6)+b}}}
{{{6=-24/5+b}}} ----> {{{b=6+24/5=(30+24)/5=54/5}}} Y-Intercept
The Line Eqn follows===> y=(4/5)x+(54/5), Or in Standard From, (-4/5)x+y=54/5. Remove fraction by multiplying the eqn by "5": 
<font color=red>-4x+5y=54</font> , Answer


Thank you,
Jojo</font>