Lets assume that you have a graph with a shaded region bounded by the line segments with endpoints (0,3),(0,9),(15/2,9/2),(10,0) and (3,0) (forming a pentagonal shaded region.)(See attachment.))
Using the endpoints to find the slope and then finding the equations of the lines that contain the segments we get:
We need to convert these equations into inequalities to form the given shaded region. First note that if the given line/line segment is dotted then the inequality is strict (either < or >) while if the line/line segment is solid the inequality is inclusive (`<=, >=` ).
To determine if an inequality is less than (or less than or equal to) we note that each such inequality divides the plane into two half-planes. On one side of the line are all solutions to the inequality while the other side has no solutions.
So consider the "line" x+y=3. The point (4,4) is in our shaded region and therefore is a solution to the inequality. Note that if x=4 and y=4 we get 4+4>3 so the inequality must be `x+y>3 "or" x+y >= 3` where the determining factor for whether the inequality is strict or inclusive depends on if the line x+y=3 is solid or dotted.
We continue for each equation:
9(4)+5(4)<90 so we want `9x+5y<90 " or " 9x+5y <= 90`
3(4)+5(4)<45 so we want `3x+5y<45 " or "3x+5y<=45 `
Since 4>0 we want `x>0 " or " x>=0` and `y>0 " or " y>=0`
If the shaded region is not the central pentagon but some other region we proceed as above. Find the equations of the bounding lines and write as inequalities so that a point in the shaded region is a solution to the inequality.