Question 198818
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Given Line Eqn, {{{4x+y=6}}} ---> {{{y=highlight(-4)x+6}}} has a Slope=m= -4.


Paralle Lines have the same Slope, {{{m[1]=m[2]}}}


Then, thru point (1,3) via Slope-Interecpt Form,
{{{y=mx+b}}}
{{{3=(-4)(1)+b}}}
{{{3=-4+b}}} ===> {{{b=3+4=red(7)}}}, Y-Intercept


It follows ---> {{{red(y=-4x+7)}}}, or {{{red(4x+y=7)}}}, Std Form


Let Fy=0:
{{{4x+0=7}}} ----> {{{cross(4)x/cross(4)=7/4}}} ---> {{{x=7/4}}}, X-Intercept
(7/4,0)  or   (1.75,0)


Let Fx=0:
{{{4(0)y=7}}}
{{{y=7}}}, Y-Intercept



{{{drawing(300,300,-3,5,-5,10,grid(1),graph(300,300,-3,5,-5,10,-4x+7,-4x+6),green(circle(1,3,.15)),blue(circle(7/4,0,.10)),blue(circle(0,7,.10)))}}} ---> {{{red(4x+y=7)}}}; {{{green(4x+y=6)}}}


Thank you,
Jojo</font>