Question 840516
FIND BOUNDARY LINE


y=mx+b
{{{m=(8-(-16))/(1-(-7))=24/8=3}}}
{{{m=3}}}.
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Take either point of the line,
b=y-mx
{{{b=8-3*1}}}
{{{b=5}}}
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Boundary Line, {{{highlight_green(y=3x+5)}}}



EXAMINING NON-SOLUTION POINTS FOR INEQUALITY

Intuition leads me to want Standard Form for this.
{{{-3x+y=5}}}.
Test the non-solution point to find if it gives left side member greater than or less than 5.  Also be sure to find if it is on the boundary or not on the boundary.
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Are (-7,0) and  (3,14) on the boundary?
POINT (-7,0):{{{-3*(-7)+0=5}}}
{{{21=5}}}, No.
POINT (3,14): {{{-3*3+14=5}}}
{{{14-9=5}}}, Yes.
Now we know, because (3,14) is ON the line and NOT a solution, we have a strict inequality.  The line does NOT contain points of the inequality solution.
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Look again at the non-solution point (-7,0).
When tested in -3x+y versus 5 what was found was {{{-3x+y>5}}},
So THAT is the inequality we find.
{{{highlight(highlight(-3x+y>5))}}}.
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Unless teacher or book specifies differently, the choice of keeping in standard form or making into slope-intercept form is yours.  You could report, {{{y>3x+5}}}.