Question 189761
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Given: m=4/5,(4,-9)


Via Slope-Intercept Form, y=mx+b


Finding y-intercept "b":


{{{-9=(4/5)(4)+b}}}
{{{-9=(16/5)+b}}}
{{{-9-(16/5)=b}}}
{{{(-45-16)/5=b}}}
{{{red(b=-61/5)}}}, y-Intercept (0,-61/5)


It follows ---> {{{highlight(y=(4/5)x-61/5)}}} or 
{{{(-4/5)x+y+61/5=0}}} ---> {{{highlight(-4x+5y+61=0)}}}, Standard Form (Answer)


To verify, we'll get the intercepts:
Let Fy=0 ----> {{{-4x+5(0)+61=0}}}
{{{-4x=-61}}} ---> {{{cross(-4)x/cross(-4)=-61/-4}}}
{{{red(x=61/4)}}}, x-Intercept (61/4,0) or (15.25,0)


Let Fx=0 ---> {{{-4(0)+5y+61=0}}}
{{{5y=-61}}} ---> {{{cross(5)y/cross(5)=-61/5}}}
{{{red(y=-61/5)}}},y-Intercept (0,-61/5) or (0,-12.2)


As we see,
{{{drawing(400,400,-5,18,-16,5,graph(400,400,-5,18,-16,5,(4/5)x-61/5),blue(circle(61/4,0,.20)),blue(circle(0,-61/5,.20)),green(circle(61/4,0,.15)),green(circle(0,-61/5,.15)))}}}


Thank you,
Jojo</font>