Question 120530



Start with the given inequality:


{{{y>=1}}}


Set up a number line:

{{{number_line(500,-9,11)}}} note: just replace the x with the variable you are working with



Now plot the point {{{y=1}}} on the number line



{{{number_line(500,-9,11, 1)}}}



Now pick any test point you want, I'm going to choose y=0, and test the inequality {{{y>=1}}}



{{{0>=1}}} Plug in {{{y=0}}}



Since this inequality is <font size=4><b>not</b></font> true, we simply shade the entire portion that does <font size=4><b>not</b></font> contain the point y=0 using the point {{{y=1}}} as the boundary. This means we shade everything to the right of the point {{{y=1}}} like this:

{{{drawing(500,50,-9,11,-10,10,
number_line(500,-9,11, 1),
blue(line(1,-5,1+10,-5)),
blue(line(1,-6,1+10,-6)),
blue(line(1,-7,1+10,-7)),
blue(arrow(1,-5,1+10.2,-5)),
blue(arrow(1,-5.5,1+10.2,-5.5)),
blue(arrow(1,-6,1+10.2,-6))
)}}} Graph of {{{y>=1}}} with the shaded region in blue

note: at the point {{{y=1}}}, there is an <font size=4><b>closed</b></font> circle. This means the point {{{y=1}}} is included from the solution set.