Question

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Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:

y > −2x + 3
y is less than 1 over 2 times x minus 2

Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)

Part B: Is the point (−2, 3) included in the solution area for the system? Justify your answer mathematically. (4 points)

Answer 1

A graphing calculator can be helpful for these.

A) Since neither inequality includes the "or equal to" case, the boundary line for the solution set is a dashed line. For the first inequality, the shading is above the line; for the second, the shading is below the line. The solution set is points to the right of perpendicular lines with slope -2 and +1/2 through point (2, -1).

B) The point -2, 3 satisfies, neither inequality.
.. 3 > -2(-2) +3 . . . FALSE
.. 3 < 1/2(-2) -2 . . .FALSE