Graphing Inequalities and Feasible Regions

The video tutorial explains how to graph a feasible region defined by four inequalities. It involves graphing each inequality, shading the appropriate regions, and identifying the area that satisfies all inequalities. The tutorial covers the process of determining intercepts using T-tables and testing points to decide shading directions. The final feasible region is a quadrilateral formed by the intersection of the shaded areas.

What is the purpose of graphing the feasible region?

• To find the area where all inequalities are satisfied

• To calculate the slope of a line

• To determine the maximum value of a function

• To identify the intersection of two lines

Which line represents the boundary for inequality 3?

• Line Y = 0

• Line X = 0

• X-axis

• Y-axis

For inequality 4, where do we shade the region?

• To the right of the vertical line

• To the left of the vertical line

• Above the horizontal line

• Below the horizontal line

What is the Y-intercept of the line 3X + 5Y = 45?

• (0, 9)

• (0, 15)

• (15, 0)

• (9, 0)

How do you determine where to shade for inequality 1?

• By using the distance formula

• By calculating the midpoint of the line

• By finding the slope of the line

• By checking if the origin satisfies the inequality

What is the X-intercept of the line 6X + Y = 36?

• (0, 6)

• (36, 0)

• (6, 0)

• (0, 36)

Which point is used to test the shading for inequality 2?

• (0, 0)

• (1, 1)

• (6, 0)

• (0, 36)

What shape is the feasible region in this problem?

• Triangle

• Quadrilateral

• Rectangle

• Circle

Which lines bound the feasible region?

• Green vertical, orange horizontal, blue, and black lines

• Red vertical, yellow horizontal, blue, and black lines

• Green horizontal, orange vertical, blue, and red lines

• Yellow vertical, green horizontal, red, and blue lines

What does the feasible region represent?

• The area under a curve

• The intersection of two lines

• The maximum value of a function

• All ordered pairs that satisfy all inequalities