Answer:
6. Ethan should shade the region marked B
7. No, point (0, 4) will not be included in the solution set
8. Point (0, -2) will not be included in the solution set
Explanation:
Let us explain how to solve the question
The graph represents the equation 2x - 5y = 10
The inequality is 2x - 5y > 10
The sign of inequality is greater than without equal, that means the line represents it must be a dotted line because all the points on the line do not belong to the solution set of the inequality.
To find the area of the solution you must put y on a side and the other term on the other side
∵ 2x - 5y > 10
→ Add 5y to both sides to move y in the other side
∴ 2x - 5y + 5y > 10 + 5y
∴ 2x > 10 + 5y
→ Subtract 10 from both sides to move 10 to the other side
∵ 2x - 10 > 10 - 10 + 5y
∴ 2x - 10 > 5y
→ That means 5y < 2x - 10
∴ 5y < 2x - 10
6.
→ y < that means the area of the solutions is under the line
∴ The solutions of the inequality lie in area B
∴ Ethan should shade the region marked B
7.
∵ Point (0, 4) lies above the line in the region marked A
→ That means it does not lie in the area of the solutions
∴ Point (0, 4) will not be included in the solution set
8.
∵ Point (0, -2) lies on the line
∵ All the point on the line did not belong to the solution set as we
said before
∴ Point (0, -2) will not be included in the solution set