Question 193883
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Given Line Eqn: 5x+4y = 12 


Via Slope-Iintercept Form,{{{system(y=mx+b)}}}, where{{{system(m=Slope,b=Yintercept)}}}


Continuing,
{{{5x+4y=12}}}
{{{4y=-5x+12}}}
{{{cross(4)y/cross(4)=(-5x+12)/4=(-5/4)x+12/4}}}
reduced to,
{{{red(y=(-5/4)x+3)}}}

{{{b=3}}}, Y-Intercept,
{{{m=-5/4}}}, Slope


See graph,
{{{drawing(300,300,-6,6,-6,6,grid(1),graph(300,300,-6,6,-6,6,(-5/4)x+3),blue(circle(0,3,.15)),green(circle(4,-2,.14)))}}}--->You can see the {{{Slope=m=-5/4=DELTA(y)/DELTA(x)}}}. 
From the Y-intercept (0,3), 4 steps to the right, then 5 steps down you get next point (4,-2).


Thank you,
Jojo</font>