Please help and answer properly

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

Step-by-step 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

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x