Question 984266
You can start with standard form.


ax+by=c
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This part removed because of unknown mistake---


BETTER......
You can also start with slope-intercept form.
{{{y=mx+b}}}, and you are given b.
{{{y=mx-2}}}
Now find the slope using the two intercepts.
{{{m=(0-(-2))/(4-0)}}}
{{{m=-2/4}}}
{{{m=-1/2}}}
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The equation should be  {{{highlight(y=-x/2-2)}}}.  The slope-intercept equation  for those two axis intercept points.  


Point-slope form?
Pick either intercept point and fill in  y-v=m(x-u) and after substituting the values, keep in this format.
{{{highlight(y-(-2)=-(1/2)(x-0))}}}-----the y-intercept used here
or equivalently
{{{highlight(y+2=-(1/2)x)}}}


Look again at the slope-intercept form found:
{{{y=-x/2-2}}}
Transform into standard form.
{{{2y=-x-4}}}
{{{x+2y=-4}}}