Algebra

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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.
y=y1+m(x-x1)
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
    b=3-22/9=5/9
    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...
    9=8*7/5+b
    b=9-56/5=-11/5
    and the solution set is below the line,or
    y<8x/5-11/5
    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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