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Write a system of inequalities to describe the shaded area of the graph.

This is the question on my homework today that i just don't get. My teacher said to use point slope form.
The coordianate points of the triangular area are
line 1: (2,1),(7,9)
line 2: (7,9),(11,3)
line 3: (2,1), (11,3)
(i wish that i could just show you the graph.
Kay, so i know that lines 1 and 2 are going to be less than or equal to, and line 3 will be greater than or equal to. However, after I put it into the formula, (which i don't think i got quite right) i don't know if that's the final part of writing the system.
for line 1, i think that i got something like:
(7,9) y=9+8/5(x-7)
Is this right? Also, is this the last part of making this fit into a system?(i think it looks too wierd to leave like that) Any help or tips is VERY much appreciated. Thanks.

  • Algebra -

    I assume the acceptable values are in the triangle.

    so for the bottom line:
    y=mx+b the two points are 2,1 and 11,3
    y=2/9 x+ b ( m= (y1-y2)/(x1-x2)
    then to solve for b
    3=2/9 *11 + b
    so the solution area here, is all above the line, or y>2x/9 + 5/9

    Now consider the left line
    y=mx+ b (m= (9-1)/7-2)=8/5
    y=8x/5+b solve for b...
    and the solution set is below the line,or
    Then to the last line the same way, the solution set will be below that line.

    Those three equations are your system of inequalities.

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