Question 817962
You probably graph {{{y=2x-3}}} ,in slope-intercept form,
by starting with the y-intercept, point (0,-3),
and using the slope, 2, to mark all the other points,
knowing that as x increases by 1, y would increase by 2.
 
{{{y-1=(1/4)(x+5)}}} is in what we call point-slope form,
meaning that it tells you that the line goes through point (-5,1),
and has a slope of 1/4.
Look at it this way:
{{{y-1=(1/4)(x+5)}}}<-->{{{(y-1)/(x+5)=1/4}}}<-->{{{(y-1)/(x-(-5))=1/4=slope}}} .
 
You can start from point (-5,1),and know that
for every 1 unit increase in x, there is a 1/4 increase in y,
or for every 4 unit increase in x, there is a 1 unit increase in y.
 
{{{drawing(300,300,-7,3,-5,5,
grid(1), green(circle(-5,1,0.2)),
blue(line(-9,0,3,3))
)}}}