To determine which ordered pairs satisfy the inequality $y > 7x - 3$, let's evaluate each option by substituting the values of $x$ and $y$ into the inequality:

Given Inequality:

$y > 7x - 3$

Checking Each Option:

Option A: $(2, 15)$

1. Substitute $x = 2$ and $y = 15$ into $y > 7x - 3$.
2. Calculate $7 \cdot 2 - 3 = 14 - 3 = 11$.
3. Check if $15 > 11$, which is true.

Option B: $(-3, -15)$

1. Substitute $x = -3$ and $y = -15$ into $y > 7x - 3$.
2. Calculate $7 \cdot (-3) - 3 = -21 - 3 = -24$.
3. Check if $-15 > -24$, which is true.

Option C: $(0, -3)$

1. Substitute $x = 0$ and $y = -3$ into $y > 7x - 3$.
2. Calculate $7 \cdot 0 - 3 = 0 - 3 = -3$.
3. Check if $-3 > -3$, which is false (since it’s equal, not greater).

Option D: $(1, 5)$

1. Substitute $x = 1$ and $y = 5$ into $y > 7x - 3$.
2. Calculate $7 \cdot 1 - 3 = 7 - 3 = 4$.
3. Check if $5 > 4$, which is true.

Option E: $(-2, -18)$

1. Substitute $x = -2$ and $y = -18$ into $y > 7x - 3$.
2. Calculate $7 \cdot (-2) - 3 = -14 - 3 = -17$.
3. Check if $-18 > -17$, which is false.

Conclusion:

The ordered pairs that satisfy the inequality $y > 7x - 3$ are:

• A. (2, 15)
• B. (-3, -15)
• D. (1, 5)

Would you like further details on any specific steps or have questions about this solution?

Here are some additional questions that might expand your understanding:

1. How do we determine the region of solutions for linear inequalities on a graph?
2. What would change if the inequality was $y \geq 7x - 3$?
3. How can we verify solutions to inequalities algebraically versus graphically?
4. How does the slope and intercept in $y > 7x - 3$ affect the solution set?
5. What methods are available to solve systems of linear inequalities?

Tip: When solving inequalities, always substitute values to check if they satisfy the inequality fully, as the answer can hinge on strict versus non-strict inequality signs.