Let's solve this inequality:

Given inequality:

$y \geq 2x - 1$

We need to check which of the given points satisfies this inequality.

Option A: $(4, 2)$

Substitute $x = 4$ and $y = 2$ into the inequality: $2 \geq 2(4) - 1$ $2 \geq 8 - 1$ $2 \geq 7 \quad \text{(false)}$ So, option A is not a solution.

Option B: $(4, 1)$

Substitute $x = 4$ and $y = 1$: $1 \geq 2(4) - 1$ $1 \geq 8 - 1$ $1 \geq 7 \quad \text{(false)}$ So, option B is not a solution.

Option C: $(0, -10)$

Substitute $x = 0$ and $y = -10$: $-10 \geq 2(0) - 1$ $-10 \geq -1 \quad \text{(false)}$ So, option C is not a solution.

Option D: $(0, 2)$

Substitute $x = 0$ and $y = 2$: $2 \geq 2(0) - 1$ $2 \geq -1 \quad \text{(true)}$ So, option D is a solution.

Final Answer:

The correct solution is D. (0, 2).

Would you like further details on solving inequalities or have any other questions?

Here are 5 related questions to explore:

1. How do you graph the inequality $y \geq 2x - 1$?
2. How do you determine if a point lies on the boundary line of an inequality?
3. What is the difference between $y \geq 2x - 1$ and $y > 2x - 1$?
4. How do inequalities change when multiplying by a negative number?
5. How can we test points to check if they satisfy a system of inequalities?

Tip: Always test points by substituting them directly into the inequality to check if they satisfy the condition!