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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.

Which of the following ordered pairs is part of the solution set for the equation y = 2x + 5?

Learn how to determine which ordered pair is part of the solution set for the linear equation y = 2x + 5. The solution involves key algebraic concepts and substitution. Suitable for students in Grades 7-9.

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