Question

Use 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

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

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

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

(3,−1)

Answer 1

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

1. **For \( (1, 7) \)**:
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(Matches)}
\]

2. **For \( (1, 2) \)**:
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(Does not match)}
\]

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

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

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

Therefore, the correct response is \( (1, 7) \).