Question

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 2 y is greater than or equal to negative 5 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, −2) included in the solution area for the system? Justify your answer mathematically. (4 points)

Answer 1

The graph is shown in the attachment.

Part A

The boundary of the solution area for the first inequality is a dashed line with slope +4 and y-intercept of -2. The solution area is below and to the right of the line. The line is not part of the solution space.

The boundary of the solution area for the second inequality is a solid line with slope -5/2 and y-intercept of -2. The solution area is above and to the right of the line. The line is part of the solution space.

The solution area is the intersection of the two shaded areas, so is the space generally to the right of the < shape defined by the two lines. The point of the < is the intersection point of the two lines, at (x, y) = (0, -2).

Part B

The point (-2, -2) is to the left of the left-most point of the solution, (0, -2), so is NOT in the solution area. It does not satisfy the first inequality, for example.

$-2\nless 4\cdot (-2)-2\\{-2}\nless -10$