Question

Which of the following options represents the vertices of the region defined by the inequalities: y > 3x - 7, y < 8, and x + y > 1?

A) (0, 0), (2, 6), (4, 8)
B) (-1, 2), (0, 7), (2, 6)
C) (1, 0), (3, 4), (5, 6)
D) (-2, 1), (0, 8), (3, 5)

Answer 1

The vertices of the region can be found by graphing the lines represented by each inequality and identifying the points of intersection. The correct option is (1, 0), (3, 4), and (5, 6).

Step-by-step explanation:

The vertices of the region defined by the inequalities y > 3x - 7, y < 8, and x + y > 1 can be found by graphing the lines represented by each inequality and identifying the points of intersection.

The inequalities can be rewritten in slope-intercept form:

• y > 3x - 7
• y < 8
• x + y > 1

By graphing these lines, we can find the region bounded by the inequalities. The correct option that represents the vertices of this region is (1, 0), (3, 4), and (5, 6).