Graphing Solutions with Polygon Tool

The video tutorial explains how to graph the solution set of a system of equations using a polygon tool. It covers graphing individual equations, identifying intercepts, and testing points to determine the correct solution region. The process involves finding intersection points and ensuring the selected region satisfies all inequalities. The tutorial concludes with a summary of the steps to identify and connect the corner points of the solution region.

What is the main objective of the problem discussed in the video?

• To solve a system of equations algebraically

• To graph the solution set using a polygon tool

• To find the roots of a quadratic equation

• To calculate the area of a polygon

How does the polygon tool help in graphing the solution set?

• By allowing users to click points to form a polygon

• By providing a list of possible solutions

• By calculating the area of the solution region

• By automatically drawing the solution region

What is the first step in graphing the equation 2x + 3y ≤ 12?

• Solving for y in terms of x

• Finding the x and y intercepts

• Calculating the area under the curve

• Finding the slope of the line

What are the intercepts of the line 2x + 3y = 12?

• (0, 6) and (4, 0)

• (0, 3) and (6, 0)

• (0, 4) and (3, 0)

• (0, 4) and (6, 0)

How many regions are created by the intersection of the two lines?

• Four

• Five

• Three

• Two

Which point is tested to determine if the large region is part of the solution set?

• (3, 3)

• (0, 0)

• (10, 10)

• (5, 5)

What conclusion is drawn from testing the point (10, 10) in the first equation?

• It satisfies the equation

• It does not satisfy the equation

• It is outside the graph

• It is the intersection point

What is the intersection point of the two lines?

• (1, 4)

• (4, 1)

• (3, 2)

• (2, 3)

Which point is confirmed to be part of the solution region after testing in the second equation?

• (3, 3)

• (2, 2)

• (4, 4)

• (1, 1)

What are the final corner points of the polygon that represents the solution region?

• (0, 0), (3, 0), (0, 3), (2, 2)

• (0, 0), (4, 0), (0, 4), (3, 2)

• (0, 0), (5, 0), (0, 5), (2, 3)

• (1, 1), (4, 1), (1, 4), (3, 2)