Use the image to answer the question.

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

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

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

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

Answer 1

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

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

2. For \( (7, 1) \): \[ y = 2(7) + 5 = 14 + 5 = 19 \quad \text{(This pair does not work.)} \]

3. For \( (1, 2) \): \[ y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(This pair does not work.)} \]

4. For \( (3, -1) \): \[ y = 2(3) + 5 = 6 + 5 = 11 \quad \text{(This pair does not work.)} \]

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

Therefore, the answer is:

(1, 7)