To solve this problem, we need to determine which of the given ordered pairs satisfies the equation $y = 2x + 5$. For each pair, we will substitute the values of $x$ and $y$ into the equation and check if it holds true.

The equation is: $y = 2x + 5$

Let's check each option:

1. For (1, 2): $y = 2 \times 1 + 5 = 2 + 5 = 7 \quad (\text{but } y = 2) \quad \text{FALSE}$

2. For (1, 7): $y = 2 \times 1 + 5 = 2 + 5 = 7 \quad (\text{and } y = 7) \quad \text{TRUE}$

3. For (3, -1): $y = 2 \times 3 + 5 = 6 + 5 = 11 \quad (\text{but } y = -1) \quad \text{FALSE}$

4. For (7, 1): $y = 2 \times 7 + 5 = 14 + 5 = 19 \quad (\text{but } y = 1) \quad \text{FALSE}$

The ordered pair $(1, 7)$ satisfies the equation $y = 2x + 5$.

Answer: $(1, 7)$

Do you want further details or have any questions?

Here are five related questions for further practice:

1. How do you determine if an ordered pair is a solution to a linear equation?
2. What is the slope and y-intercept of the equation $y = 2x + 5$?
3. How do you graph the equation $y = 2x + 5$ on a coordinate plane?
4. What is the solution to the equation $y = 2x + 5$ when $x = -3$?
5. Can you find another ordered pair that satisfies the equation $y = 2x + 5$?

Tip:

When checking whether an ordered pair satisfies an equation, always substitute both the $x$ and $y$ values and see if the equation remains true.