Question

se the image to answer the question.

A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. A line passes through the first, second, and third quadrants.

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

(1 point)
Responses

(3,−1)
left parenthesis 3 comma negative 1 right parenthesis

(1,7)
left parenthesis 1 comma 7 right parenthesis

(7,1)
left parenthesis 7 comma 1 right parenthesis

(1,2)
left parenthesis 1 comma 2 right parenthesis
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Answer 1

To determine which ordered pair is part of the solution set for the equation \( y = 2x + 5 \), we can substitute the x-coordinate of each ordered pair into the equation and see if it produces the corresponding y-value.

1. **For \( (3, -1) \)**:
- Substitute \( x = 3 \):
\[
y = 2(3) + 5 = 6 + 5 = 11 \quad \text{(not } -1\text{)}
\]

2. **For \( (1, 7) \)**:
- Substitute \( x = 1 \):
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(this works)}
\]

3. **For \( (7, 1) \)**:
- Substitute \( x = 7 \):
\[
y = 2(7) + 5 = 14 + 5 = 19 \quad \text{(not } 1\text{)}
\]

4. **For \( (1, 2) \)**:
- Substitute \( x = 1 \):
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(not } 2\text{)}
\]

The only ordered pair that satisfies the equation \( y = 2x + 5 \) is \( (1, 7) \).

Therefore, the answer is:
**(1, 7)**.