We are given the inequality:

$y + 3 > \frac{5}{2}(x - 6)$

We need to determine which of the following points satisfies this inequality.

Steps:

1. Rewrite the inequality by isolating $y$: $y > \frac{5}{2}(x - 6) - 3$ Simplifying the right side: $y > \frac{5}{2}x - 15 - 3$ $y > \frac{5}{2}x - 18$

Now, we will substitute each point into this inequality to see which one satisfies it.

Option 1: $(8, 0)$

Substitute $x = 8$ and $y = 0$ into the inequality:

$0 > \frac{5}{2}(8) - 18$ $0 > 20 - 18$ $0 > 2$

This is false.

Option 2: $(10, 4)$

Substitute $x = 10$ and $y = 4$ into the inequality:

$4 > \frac{5}{2}(10) - 18$ $4 > 25 - 18$ $4 > 7$

This is false.

Option 3: $(0, -15)$

Substitute $x = 0$ and $y = -15$ into the inequality:

$-15 > \frac{5}{2}(0) - 18$ $-15 > -18$

This is true.

Conclusion:

The only point that satisfies the inequality is $(0, -15)$.

So, the correct answer is $(0, -15)$.

Would you like further clarification or details? Here are 5 follow-up questions related to this problem:

1. How do we determine if an inequality is strict or non-strict?
2. How would the solution change if the inequality was $y + 3 \geq \frac{5}{2}(x - 6)$?
3. What is the geometric interpretation of this inequality on a coordinate plane?
4. How do we handle fractional coefficients in inequalities when solving for $y$?
5. What happens to the inequality sign when multiplying or dividing by a negative number?

Tip: When solving inequalities involving fractions, it's helpful to first isolate the variable of interest (e.g., $y$) and then substitute the values to check for correctness.